FROHLICH, Albrecht v2

FROHLICH_ALBRECHT_v2

Catalogue of the papers and correspondenceof Albrecht Frohlich FRS (1916-2001) by Timothy E. Powell and Peter Harper NCUACScatalogue no. 153/3/07 A. Frohlich NCUACS 153/3/07 Title: Catalogue of the papers and correspondence ofAlbrecht Frohlich (1916-2001), mathematician Compiled by: Timothy E. Powell and Peter Harper Description level: Fonds Date of material: 1948-2006 Extent of material: 21 boxes, ca 460 items Deposited in: College Archives, King’s College London Reference code: GB 0100 KCLCA K/PP156 © 2007 National Cataloguing Unit for the Archives of Contemporary Scientists, University of Bath. NCUACScatalogue no. 153/3/07 A. Frohlich NCUACS 153/3/07 The workof the National Cataloguing Unit for the Archives of Contemporary Scientists in the production of this catalogue is madepossible by the support of the iene y Arts & Humanities Research Council A. Fréhlich NCUACS 153/3/07 NOT ALL THE MATERIALIN THIS COLLECTION MAY YET BE AVAILABLE FOR CONSULTATION. ENQUIRIES SHOULD BE ADDRESSED IN THE FIRST INSTANCE TO: THE COLLEGE ARCHIVIST KING’S COLLEGE LONDON A. Frohlich NCUACS 153/3/07 LIST OF CONTENTS Items Page GENERAL INTRODUCTION SECTION A BIOGRAPHICAL SECTION B RESEARCH SECTION C PUBLICATIONS A.1-A.37 B.1-B.101 C.1-C.125 SECTION D VISITS, CONFERENCES AND LECTURES D.1-D.43 SECTION E CORRESPONDENCE E.1-E.125 SECTION F THESES AND EXAMINATIONS F.1-F.33 INDEX OF CORRESPONDENTS 16 25 43 51 70 74 A. Frohlich NCUACS 153/3/07 GENERAL INTRODUCTION PROVENANCE 5 The archive was received for cataloguing from Dr Ruth Frohlich, widow of Albrecht Frohlich, in February 2005 and April 2007. OUTLINE OF THE CAREER OF ALBRECHT FROHLICH Frohlich was born on 22 May 1916 in Munich, Germany to Julius and Frieda Frohlich. The family were Jewish and Julius Frohlich was a cattle merchant. Albrecht was the youngest of three children. The eldest, his sister Betti, settled in Palestine in the 1920s and his elder brother Herbert was to become a distinguished physicist. After elementary school Frohlich went to the Wittelsbacher Gymnasium but with the rise to power of the Nazis Frohlich and his parents left Germany for France in 1933, and the following year moved to Palestine to join Betti (Herbert had gone to the University of Leningrad in 1934, then to the University of Bristol in 1935). In Palestine Frohlich worked as a plumber and then as an electrician in a railway workshop. Frohlich had ended his formal education at the age of seventeen when he fled Germany. However,in 1945 Herbert, now Reader in Physics at the University of Bristol, arranged for his younger brother to join him at Bristol. Frohlich was accepted as a student and began his studies in mathematics in December 1945. He graduated with First Class Honours in 1948 and began post-graduate research under H.A. Heilbronn. Frohlich completed his doctoral thesis in October 1950 (Ph.D. awarded 1951). While an undergraduate at Bristol Frohlich met a medical student, Ruth Brooks, whom he married in 1950. She became a doctor in general practice, while also accompanying her husband on many of his visits abroad and bringing up their children. Frohlich was Assistant Lecturer in Mathematics at the University of Leicester 1950-1952 and Lecturer in Pure Mathematics at the University College of North Staffordshire 1952-1955. In 1955 he was appointed Reader in Mathematics at King’s College London. Subsequently he became Professorof Mathematics at King’s (1962), Head of Department (1969) and, on retirement, Emeritus Professor (1981). He remained active in post-retirement research and appointments included Fellowship of Robinson College, Cambridge in 1982 (Emeritus Fellow 1984) and a Senior Research Fellowship at Imperial College London 1982. During his career Frohlich held numerous Visiting Professorships, enjoying a particularly close relationship with the University of Bordeaux (Visiting Professor 1975 and 1984). He also made manyconferencevisits to the USA, Germany and France. A. Frohlich NCUACS 153/3/07 6 Fréhlich’s contributions to algebraic number theory and to mathematics more widely were acknowledgedin the citation for the de Morgan Medal of the London Mathematical Society, awarded in 1992 (A.34). ‘His research is characterised by a prodigious flow of highly original ideas, whichstill shows no sign of stopping. His work includes such topics as class two nilpotent Galois groups, class groups of abelian fields, genus theory, quadratic forms and orthogonal representations, and local Langlands theory. However, without any doubt his most important achievementis the creation of that body of knowledge now known asarithmetic Galois module theory: this seeks to exploit and develop the mysterious and wonderful relationship between certain analytic invariants, called Artin root numbers, and the purely arithmetic problem of determining the structure of the ring of integers of a Galois extension of number fields over the integral group ring of the Galois group. Although there were a few previous results due to Hilbert and Noether, the subject really took off with Frohlich's seminal work on tame Hs-extensions. Building on this, he then proceeded to develop a general theory and, in the process, produced a whole fund of new ideas and techniques. Through his work and direction this subject has helped keep British number theory at the forefront of mainstream research. Frohlich has greatly influenced the developmentof algebraic number theory in many ways; he has published seven books, written over a hundred papers and, jointly with J.W.S. Cassels, he organised the renowned Brighton conference which did so much to makeclassfield theory more widely accessible. Special mention should be made of the help and encouragementthat he has consistently given to young mathematicians: in addition to his many own research students, there have been many French and German students to whom he has provided considerable help. His enthusiasm and love for mathematics are a sourceofinspiration to all who have worked with him’. In addition to the de Morgan Medal of the London Mathematical Society, he had also received the Society’s Senior Berwick Prize in 1976. Frohlich received honorary doctorates from the universities of Bordeaux (1986) and Bristol (1998) and the Alexander von Humboldt Foundation Humboldt Research Award for the Scientific Cooperation between Great Britain and Germany in 1992. He was elected a Fellow of the Royal Sociéty in 1976. He died 8 November 2001. For a full account of Frohlich’s life and works see ‘Albrecht Frohlich (22 May 1916 - 8 November 2001)’ by B.J. Birch and M.J. Taylor, Biographical Memoirs of Fellows of the Royal Society vol 51 (2005), 149-168. A copyis atA.6. A. Fréhlich NCUACS 153/3/07 7 DESCRIPTION OF THE COLLECTION This collection dates entirely from the period after Frohlich’s arrival in Britain in 1945. It is particularly rich in documenting his mathematical researches, including mathematical workings, publications and correspondencewith colleagues. Section A, Biographical, includes obituaries and memoirs, material from the Celebration of Frohlich’s life, held in the Chapel of Robinson College Cambridge, 10 February 2002, and other tributes. The career, honours and awards subsection includes his Ph.D. thesis ‘On sometopics in the theory of representation of groups and in class field theory’, and correspondence and papers relating to his university appointments and some ofhis principal honours, including election to the Fellowship of the Royal Society. Section B, Research, is chiefly mathematical workings, notes and drafts, mostly manuscript but some typescript, presented as far as possible in alphabetical order by heading or topic. Some of the material was found in titled folders or envelopes, but much was loose. The material often comprises a number of short paginated sequences, and it is possible some were written as early drafts for publication. Few are dated but the span appears to cover Frohlich’s research career and includes work on Galois module theory and Gauss sums. The largest component is material relating to work on the decomposition of primes. Although undated this appears to be work probably begun in the 1950s. Section C, Publications, presents comprehensive documentation of Frdhlich’s published output, from his first article ‘The representation of a finite group as a group of automorphisms ona finite Abelian group’, Quarterly Journal of Mathematics 2nd ser. vol. 1 (1950), to ‘Equivariant Brauer groups’ (with C.T.C. Wall), Contemporary Mathematics vol. 272 (2000). The largest single body relates to ‘Strict factorisability and shadows’, in Algebra and Number Theory, Essen 1992 (ed. G. Frey and J. Ritter), 1994. References are made to the Bibliography at A.16 in the form Bibliog. no. .... The material mainly takes the form of offprints, but there are also some drafts of papers and occasionally accompanying mathematical workings. The section also includes a few unpublished drafts, including work with C.T.C. Wall on Brauer groups, ‘Galois modules and the functional equation’, and a possible draft of a book on ‘mathematical theory of ostensive and consequently of empirical predicates’. Section D, Visits, conferences and lectures, provides patchy coverage of Frodhlich’s conference attendance and overseas visits 1956-1998 but includes documentation of his participation in influential mathematics meetings held at the Mathematisches Forschungsinstitut, Oberwolfach, Germany and some Visiting Professorships. The material in the main comprises invitations and programmes, and texts or abstracts of lectures delivered are few. A. Frohlich NCUACS 153/3/07 8 Section E, Correspondence, is arranged in an alphabetical sequence. It is international in scope, with many correspondents from North America, France and Germany. Correspondents particularly well represented include Frohlich’s Ph.D. supervisor H.A. Heilbronn, colleagues J.-P. Serre, Olga Taussky-Todd, S.V. Ullom and C.T.C. Wall, and former research students C.J. Bushnell, M.J. Taylor and S.M.J. Wilson. Many of the letters focus on progress of research and include discussions of problems with mathematical workings, sometimes as separate documents, and drafts of papers. Although the correspondence spans 1950-2000, the bulk dates from the 1970s-1990s. Section F, Theses and examinations, comprises a set of. theses of Ph.D. students supervised or examined by Frohlich, including his research students at King’s College (see list at F.29), together with a number of examination papers, some with Fréhlich’s manuscript calculations of answers. There is also an index of correspondents. ACKNOWLEDGEMENTS Weare grateful to Dr Ruth Frohlich for making the archive available. Timothy E. Powell Bath 2007 A. Frohlich NCUACS 153/3/07 SECTION A BIOGRAPHICAL, A.1-A.37 1948-2006 A.1-A.7 OBITUARIES AND MEMOIRS A.8-A.14 MEMORIAL SERVICE AND OTHER TRIBUTES A.15-A.18 AUTOBIOGRAPHICAL A.19-A.35 CAREER, HONOURS AND AWARDS A.36, A.37 MISCELLANEOUS A.1-A.7 OBITUARIES AND MEMOIRS 2001-2006 Frohlich died on 8 November 2001. A.1 A.2 A.3 Obituaries from The Times, 30 November 2001; and Independent, Armitage (including typescript drafts, and print-out of online version) December 2001, 24 by V. obituary Obituary for the Heidelberg Academyof Sciences, 8 March 2002, by P. Rocquette (German and English versions); draft Convocation Yearbook, ?2002; obituary for King’s College London, 22002: letter to Colin ?Bushnell re draft obituary for ‘In Touch’, King’s College London newsletter, which may relate to preceding University Bristol for of 2001 2002 Online obituary by J.J. O'Connor and E.F. Robertson from MacTutor History of Mathematics 2006 (http://www-history.mcs.st-andrews.ac.uk/Biographies/Frohlich.html) A.4-A.6 ‘Albrecht Frohlich (22 May 1916 - 8 November 2001)’ by B.J. Biographical Memoirs of Fellows of the Royal Society vol 51 (2005), 149-168 Birch and MJ. Taylor, 2005 A. Frohlich NCUACS 153/3/07 10 Biographical, A.1-A.37 A.4, A.5 Typescript drafts A6 A.7 2 folders. Offprint ‘Albrecht Frohlich 1916-2001’ by M.J. Taylor, Bulletin of the London Mathematical Society vol 38 (2006), 329-350 2006 Offprint A.8-A.14 MEMORIAL SERVICE AND OTHER TRIBUTES 2001-2006 A.8 Frohlich family letter of thanks for condolences received on Albrecht Fréhlich’s death 2001 With two letters of condolence. A.9-A.11 A.Q A.10 A.12 ‘Celebration Robinson College Cambridge, 10 February 2002 of the Frdhlich’, The Chapel, life of Ali Draft and printed Order of Service Tributes to Frohlich from colleagues L. McCulloh, P. Cassou-Nogués, J. C.B. Thomas. Ritter, V. Armitage, Correspondencearising Also includes copy of programme for Robinson College Music Society ‘Steinway Concert’, 23 June 2002, featuring ‘The Frohlich Trio’ that was formed at the service on 10 February. Report by M.J. Taylor on February 2002 Oberwolfach Conference on Arithmetic and Geometry, Orders in 2002 2002 A. Frohlich NCUACS 153/3/07 11 Biographical, A.1-A.37 dedicated to the memory of Frohlich, London Mathematical Society newsletter, April 2002 A.13 and equivariant ‘e-constants Arakelov-Euler characteristics’, Ann. Scient. Ec. Norm. Sup., 4th ser. vol. 35 (2002) by T. Chinburg, G. Pappas and M.J. Taylor, ‘Dedicated to the memory of Ali Frohlich (1916-2001), for his vision, inspiration and encouragement 2002, 2005 Letter to Ruth Frohlich from C.B. Thomas, 2005, referring to dedication of his book Representations of Finite and Lie Groupsto Albrecht Frohlich. A.14 Frohlich Prize 2002, 2006 This prize, to be awarded by the London Mathematical Society for ‘new, original and extremely innovative work in Mathematics’ was established by Ruth Frohlich in line with her husband’s wishesafter his death. Correspondence re establishment of prize, 2002, and winner for 2006 (M. Weiss). A.15-A.18 AUTOBIOGRAPHICAL 1960s-2002 A.15 A.16 A.17 A.18 Curricula vitae 1960s, 1990s Bibliography 2000 bibliography has been used in This publications in section C. referencing the Manuscriptlist of books by Frohlich. Copyof Frohlich’s entry for Personal Records of Fellows of the Royal Society; copy ofcitation of election (1976) 1976, 1987 Entry for Frohlich for International Who’s Who 2002 2002 A. Frohlich NCUACS 153/3/07 12 Biographical, A.1-A.37 A.19-A.35 CAREER, HONOURS AND AWARDS 1948-2005 A.19, A.20 Student, University of Bristol 1948-1950 Frohlich came to Bristol at the end of the Second World War at the suggestion of his brother Herbert who was Reader in Physics at the University. studies Although Frohlich had ended his formal education at the age of seventeen he wasaccepted as a student and began his mathematics in December 1945. He graduated in 1948 and began doctoral research under H.A. Heilbronn. Frohlich completed his Ph.D. thesis in October 1950 (awarded 1951). in A.19 A.20 A.21 A.22 Later account of arrival in Bristol in 1945 (photocopied manuscript); Stewart Scholarship 1948-1949; testimonials by E.H. Linfoot and H.R. Hassé; etc. notification of award John of 1948-1950 ‘On some topics in the theory of representation of groups andin classfield theory’, Ph.D. thesis, October 1950 1950 Assistant Lecturer in Mathematics, University of Leicester 1950-1951 Correspondencere appointment. Lecturer in Pure Mathematics, University College of North Staffordshire, Keele 1951-1952 Correspondencere appointment. A.23 Appointments at King’s College London 1954-1981 in Pure Reader of Mathematics (1962), Head of Department (1969), Emeritus Professor (1981). Mathematics Professor (1955), Correspondencere appointments. A. Frohlich NCUACS 153/3/07 13 Biographical, A.1-A.37 A.24-A.27 Election to the Fellowship of the Royal Society, 1976 1964-1977 Fréhlich’s citation noted, ‘Distinguished for his work in algebra and in particular in algebraic number theory. He made his reputation for his contributions to a variety of areas near-rings, homological algebra and in particular to class-field theory in a non-Abelian context. His recent investigations of the module-structure the part discovery a conjectural) with the behaviour of the associated zeta- and L-functions has attracted widespread interest’. See also A.17. of totally unsuspected procedures”, number-fields and (in relation algebraic such as_ “effective of A.24 A.25 Correspondencere proposal 1964, 1968 Notification in press; list of Fellows elected 1976 1976 A.26, A.27 Letters of congratulation 1976-1977 In chronological order. Not indexed. 2 folders. A.28 London Mathematical Society Senior Berwick Prize for 1976 1976 Correspondencere arrangements for presentation. A.29 Election to Fellowship, Robinson College Cambridge 1982 Notice from King’s College London. A.30 Leverhulme Emeritus Fellowship 1984-1989 Frohlich was awarded a Fellowship to support his ongoing research into Galois Gauss sums. Includes draft of application for Fellowship 1984, and Report to the Leverhulme Trust 1987. A. Frohlich NCUACS 153/3/07 14 Biographical, A.1-A.37 A.31 Honorary Doctorate, University of Bordeaux, March 1986 1986 Notice, letter of congratulation. A.32 Senior Research Fellow, Imperial College 1988-1996 Correspondencere appointment. A.33 Alexander von Humboldt Foundation Humboldt Research Award for the Scientific Cooperation between Great Britain and Germany, 1992 1992, 2001 Frohlich received the award ‘in recognition of your past accomplishments in research and teaching’. Correspondence. A.34 London Mathematical Society de Morgan Medal for 1992 1992, 1993 received his many important Frohlich most contributions important achievement is the creation of that body of knowledge now knownasarithmetic Galois module theory’. the medal ‘for algebraic number theory...his to Notification; short citation; full citation (in volume 25 (1993) of the Bulletin of the London Mathematical Society pp.412- 414): letters of congratulation (in chronological order, not indexed). A.35 Honorary Doctorate, University of Bristol 1998, 2005 Includes Order for Degree Congregation, 6 July 1998 and text of speeches for Honorary Graduands (see pp.25-26 for speech commending Frohlich, by A.H. Schofield). A.36, A.37 MISCELLANEOUS A.36 of Photocopy blackboard; correspondence from Ottawa, Canada re use of photograph of Frohlich, 1974 photograph at University, lecturing of Fréhlich Carleton N.d.,1974, 1975, 1981 N.d.,1974- 1975 A. Frohlich NCUACS 153/3/07 15 Biographical, A.1-A.37 A.37 ‘University cuts’, Letter published in The Times, 26 March 1981 1981 Typescript letter as sent; publishedletter. A. Fréhlich NCUACS 153/3/07 SECTION B RESEARCH, B.1-B.101 16 ?1950s- 1996, n.d. drafts presented This section is chiefly manuscript mathematical workings, notes and in alphabetical order by heading or topic title. Some were found in titled folders or envelopes, but much was loose. The material often comprises a numberof short paginated sequences, and some may have been written as early drafts for publication. Few are dated. as far as possible Frohlich’s handwriting, as he himself acknowledged in correspondence with colleagues, is not always easy to decipher. This becomes more problematic where the material is in rough form and evidently intended for his use only. B.1 B.2 ‘Absolute conductor & resolvent theory’ Contents of folder so inscribed. ‘On algebraic closure’ N.d. N.d. B.3-B.8 ‘Archimedean theory etc’ and ‘Norms’ ca 1965 B.3 B.4 B.S B.6-B.8 Bundle of folders so labelled. Some of the folders were themselves inscribed and the contents in some cases further subdivided. ‘Archimedean theory. Duality in real vector spaces’ ‘Geometry of numbers’ ‘Norms of operators’ and ‘Characters with transformations’ ‘Norms’ 3 folders. B.9 ‘Some remarks on Artin conductors’ N.d. 10pp typescript. A. Frohlich NCUACS153/3/07 17 Research, B.1-B.101 B.10, B.11 ‘Relative Brauer + Picard groups‘ and ‘Various results for changeofrings’ 1969, n.d. Contents of folder so inscribed. 1969. Some workings dated 2 folders. B.12 ‘A canonical class for Galois extensions of number fields’ N.d. Manuscript and typescript workings so titled; typescript pages and manuscript and photocopied manuscript notes found therewith. B.13 ‘Canonical factorisation and Martinet’s conjecture’ Photocopy manuscript workings sotitled, 9pp and 14pp. B.14 ‘Notesfor further work on conductors’ Contents of folder so inscribed. N.d. N.d. B.15-B.31 Decomposition 21950s Bundle of folders inscribed ‘Dec’, ‘Decomp’ and similar: work on the decomposition of primes. This was work begun by Frohlich in the 1950s and some of the material appears to have been drafted with publication in mind. ‘Decomp. 1 draft. A Frohlich’ ‘Drafts, decomp.’ ‘Dec. Chpt. 3’ ‘Dec. Chp 4’ B.15 B.16 B.17 B.18 A. Frohlich NCUACS 153/3/07 18 Research, B.1-B.101 B.19-B.22 ‘Final draft. Prime decomposition [...]’ 4 folders. ‘Dec. ‘Decomposition. Numerical examples’ ‘Dec. (a) p-adic problem. (b) local fields for p+2’ B.23 B.24 B.25 B.26, B.27 ‘Dec. details’ With later manuscript note ‘explicit calculations in number field extensions [...]’. folder (retained at B.27) bears mathematical Original working. 2 folders. B.28-B.30 ‘Notes for dec. paper’ 3 folders. B.31 ‘Dec. Local fields over R.’ With later manuscript note ‘Extensions of R2 of certain [?unipotency] classes: explicit calculations’, B.32 ‘On the density of discriminants of cubic fields II’ N.d. Typescript note with manuscript annotation. B.33 ‘'§ 2 The class of a principal factorisation’ N.d, 1996 Photocopied typescript ‘printout’; manuscript workings. manuscript and typescript draft; 4pp A. Frohlich NCUACS 153/3/07 Research, B.1-B.101 B.34, B.35 ‘First write-up concerning factorisibility’ 2 folders. B.36-B.38 ‘Fields over P2’ folder (retained at B.38) bears mathematical Original working. 3 folders. Manuscript and photocopied manuscript workings, first page beginning ‘Notions ofa filtered ring [...] ‘4 Finite fields’ Photocopied manuscript working. Manuscript working, first page beginning ‘T a finite group, B, its Burnside ring [...]’ Includes ‘Examples (I alwaysfinite), 20pp. Manuscript and photocopied manuscript workings, with later covering note ‘handwritten part of papers e e Galois Gauss sums — resolvents Galois stabil lattices’ First page is inscribed ‘Olga’. ‘Gal. Gauss Notes’ 6pp typescript progress report on work on a Galois extension N/K of number fields; manuscript working beginning ‘Here N/K is a Galois extension offields’. B.39 B.40 B.41 B.42 B.43 B.44 B.45 ‘On wild Galois extensions of number fields’ 19 N.d. N.d. 1969 N.d. N.d. N.d. N.d. 1993 N.d. A. Frohlich NCUACS 153/3/07 20 Research, B.1-B.101 B.46 ‘Reformulation of some results on Galois module structure’ N.d. Manuscript and circulation only)’. typescript drafts marked ‘(Informal B.47 ‘§ 2 Introduction to Gauss sums’ N.d. 39pp manuscript working. B.48 ‘Gauss sums’ ca 1983 Typescript draft, ‘This is a report on some aspects ofjoint workwith C.J. Bushnell’ (may relate to Gauss sums and p- adic division algebras, at C.78). B.49 ‘A programmeforelliptic Gauss sums’ This may have been intendedfor delivery as a lecture. B.50 ‘Wild Gauss sums’ B.51, B.52 ‘Genusclassfreq.’ Contents of folder so inscribed divided into two for ease of reference. B.53-B.55 ‘Graded categories’ Contents of envelope so inscribed divided into three for ease of reference. N.d. 1993 N.d. N.d. B.56-B.58 ‘Gras conjecture’ 1989, 1990 Contents of folder so inscribed divided into three for ease of reference. Includes correspondence with T.C. Chinburg and D. Burns re work on the Gras conjecture, with manuscript workings by Frohlich. A. Frohlich NCUACS 153/3/07 Research, B.1-B.101 B.59 B.60 Untitled manuscript working beginning ‘The idele group of a number field E’ ‘Integral or Radical modules. II°. Functions based on Resolvents’ Contents internally according to the folder inscription. inscribed, so of folder further subdivided B.61 ‘|-adic theory’ With later manuscript note ‘AF has defined his requlator, see the appr Crelle [?Crelle’s Journal] paper. This seems to be related (and earlier)’. B.62, B.63 ‘Local classfields and C.M.’ Contents of envelope so inscribed divided into two for ease of reference. 21 N.d. N.d. 1988 N.d. B.64 ‘Some comments on the map (’ ca 1980 7pp typescript. With later manuscript note. B.65, B.66 ‘[...] Categories of modules’ 2 folders. B.67 ‘“Monomial” Conductor’ 1p only. B.68-B.70 ‘Normswrite up Jan 77’ and ‘Main write up’. Contents of folder so inscribed. B.68 55pp typescript with list of contents N.d. N.d. 1977 A. Frohlich NCUACS 153/3/07 22 Research, B.1-B.101 B.69, B.70 Manuscript workings 2 folders. B.71, B.72 ‘Normed space’ Contents of folder so inscribed divided into two for ease of reference: typescript ‘first attempt at writing up what | know about normed modules’ by Cambridge colleague (signature unclear), 55pp typescript. B.73 ‘p-adic theory’ Contents internally by label. of folder so inscribed, further subdivided B.74 ‘A quadratic-elliptic Stickelberger element’ 11pp photocopied manuscript working not in hand. Frdéhlich’s B.75 ‘The quadratic reciprocity law’ 5pp typescript, with later manuscript note ‘an interesting (and strange) argument proving the quadratic reciprocity law)’. B.76 B.77 B.78 ‘The category of rings with operators’ ‘Resolvents’ Contents of folder so labelled. ‘Calculations with resolvents and cocycles root numbers’ Bundle of workings so labelled. N.d. N.d. N.d. N.d. N.d. N.d. N.d. A. Frohlich NCUACS 153/3/07 B.79 B.80 B.81 B.82 B.83 B.84 B.85 B.86 B.87 ‘Trace forms and related matters’ Photocopied manuscript circulation June 26, 1990’. draft marked ‘Restricted ‘The twisting factor’ ‘Weak equivalence for tame representations of the Weil- group QO of a local field F’ Untitled workings, dated 22 and 23 January 1969 Untitled working, dated 26 April 1980, with ‘Supplement to my M.S. of 26 April’ B.88-B.90 ‘Old’ Contents of folder so inscribed divided into three for ease of reference: mathematical workings. Research, B.1-B.101 ‘Siegel functions’ ‘Siegel modular forms and a candidate for a v4-periodic cohomology theory’ 5pp photocopied manuscript working not in hand. Frdhlich’s 23 N.d. 1991 ‘Proof of the strong approximation theorem by additive duality’ N.d. 2pp photocopied typescript. N.d. 1990 N.d. N.d. 1969 1980 N.d. A. Frdéhlich NCUACS 153/3/07 Research, B.1-B.101 B.91-B.93 Contents of much reused folder divided into three for ease of reference: mathematical workings B.94 B.95 ‘Some more general nonsense’ ‘§ More abstract nonsense’ Duplicated typescript paginated 99-115. B.96-B.101 Miscellaneous mathematical workings 6 folders. 24 N.d. N.d. N.d. N.d. A. Frohlich NCUACS 153/3/07 SECTION C PUBLICATIONS, C.1-C.125 25 1950-2000, n.d. The Bibliog.no. ... references in the catalogue entries refer to Frohlich’s Bibliography presented at A.16. The bulk of the material is offprints of published papers but there are also a few unpublished drafts, including work with C.T.C. Wall on Brauer groups, and a possible draft of a book and consequently of empirical predicates’. ‘mathematical theory on of ostensive C.1 C.2 C.3 C.4 C.5 C.6 ‘The representation of a finite group as a group of automorphisms ona finite Abelian group’, Q. J. Math. 2nd ser. vol. 1 (1950) 270-283. Bibliog. no. 1 1950 Offprint. ‘On the class group ofrelatively Abelian fields’, Q. J. Math. 2nd ser. vol. 3 (1952), 98-106. Bibliog. no. 2 1952 Photocopied offprint. ‘On fields of class two’, Proc. Lond. Math. Soc. 3rd ser. vol. 4 (1954), 235-256. Bibliog. no. 3 1954 Offprint. ‘On the absolute class group of Abelian fields’, J. Lond. Math. Soc. vol. 29 (1954), 211-217. Bibliog. no. 4 1954 Offprint. ‘A note on the classfield tower’, Q. J. Math. 2nd ser. vol. 5 (1954), 141-144. Bibliog. no. 5 1954 Offprint. ‘The generalization of a theorem of L. Rédei’s’, Q. UJ. Math 2nd ser. vol. 5 (1954), 130-140. Bibliog. no. 6 1954 Offprint. A. Frohlich NCUACS 153/3/07 C.7 C.8 C.9 C.10 C.12 C.13 Publications, C.1-C.125 ‘A remark on the class number of Abelian fields’. J. Lond. Math. Soc. vol. 29 (1954), 498. Bibliog. no. 7 Offprint. ‘On the absolute class group of Abelian fields (II)’. J. Lond. Math. Soc. vol. 30 (1955), 72-80. Bibliog. no. 8 Offprint. ‘Non Abelian laws of prime decomposition’, Proc. Cong. Amsterdam: North-Holland, 1955. Bibliog. no. 9 Math., Amsterdam 1954, vol. Int. 20-21. 2, pp. Offprint (of abstract). J.C. Shepherdson) of (With polynomials in a finite number of steps’, Math. Zeitschr. vol. 62 (1955), 331-334. Bibliog. no. 10 factorisation ‘On the Offprint. (With J.C. Shepherdson) ‘Effective procedures in field theory’, Phil. Trans. R. Soc. Lond. vol. A248 (1956), 407— 432. Bibliog. no. 11 Offprint. Soc. Math. ‘Distributively generated near-rings. |. Ideal theory’. Proc. Lond. vol. 8 (1958), 76-94 and ‘Distributively generated Representation theory’. Proc. Lond. Math. Soc. 3rd ser. vol. 8 (1958), 95- 108. Bibliog. nos. 12 and 13 near-rings. 3rd ser. Il. 26 1954 1955 1955 1955 1956 1958 Photocopied offprints. ‘The near ring generated by the inner automorphismsof a finite simple group’, J. Lond. Math. Soc. vol. 33 (1958), 95— 107. Bibliog. no. 14 1958 Offprint. A. Frohlich NCUACS 153/3/07 27 Publications, C.1-C.125 C.14 C.15 C.16 C.18 C.19 C.20 ‘On a method for the determination of class factors in number fields’, Mathematika vol. 4 (1957), 113-121. Bibliog. no. 15 1957 Offprint. ‘The restricted biquadratic residue symbol’, Proc. Lond. Math. Soc. 3rd ser. vol. 9 (1959), 189-207. Bibliog. no. 16 1959 Offprint. ‘The rational characterisation of certain sets of relatively Abelian extensions’, Phil. Trans. R. Soc. Lond. vol. A251 (1959), 385-425. Bibliog. no. 17 Offprint. ‘The genus field and the genus group in finite number fields’, Mathematika vol. 6 (1959), 40-45; and ‘The genus field and the genus group in finite number fields. II’, Mathematika vol. 6 (1959), 142-146. Bibliog. nos. 18 and 19 Offprints. ‘Discriminants of algebraic number fields’, Math. Zeitschr. vol. 74 (1960), 1-28; and ‘Ideals in an extension field as modules over the algebraic integers in a finite number field’, Math. Zeitschr. vol. 74 (1960), 29-38. Bibliog. nos. 20 and 21 Offprints. ‘The discriminants of relative extensions and the existence of integral bases’, Mathematika vol. 7 (1960), 15-22. Bibliog. no. 22 Offprint. ‘On groups over a d.g. near-ring (I): Sum constructs and free R-groups’, Q. J. Math. 2nd ser. vol. 11 (1960), 193- 210; and ‘On groups over a d.g. near-ring (II): Categories 1959 1959 1960 1960 1960 A. Frohlich NCUACS153/3/07 28 Publications, C.1-C.125 and functors’, Q. J. Math. 2nd ser. vol. 11 (1960), 211-228. Bibliog. nos. 23 and 24 Offprints. ‘A prime decomposition symbol for certain non-Abelian numberfields’, Acta Sci. Math. Szeged vol. 21 (1960), 229-246. Bibliog. no. 25 1960 Offprint. ‘Non Abelian Homological Algebra. |. Derived functors and satellites’, Proc. Lond. Math. Soc. 3rd ser. vol. 11 (1961), 239-275; ‘Non Abelian Homological Algebra. II. Varieties’, Proc. Lond. Math. Soc. 3rd ser. vol. 12 (1962), 1-28; and ‘Non Abelian Homological Algebra. Ill. The functors EXT and TOR’, Proc. Lond. Math. Soc. 3rd ser. vol. 12 (1962), 739-768. Bibliog. nos. 26-28 1961, 1962 Offprints. ‘On the /-class group of the field P('vmy’, J. Lond. Math. Soc. vol. 37 (1961), 189-192; ‘A remark on the class field tower of the field P(’Vm)', J. Lond. Math. Soc. vol. 37 (1961), 193-194. Bibliog. nos. 29 and 30 Offprints. ‘Discriminants and module invariants over a Dedekind domain’, Mathematika vol. 8 (1961), 170-172. Bibliog. no. 31 Offprint. module structure ‘The over Dedekind domains’, J. reine angew. Math. vol. 209 (1962), 39-53. Bibliog. no. 32 of Kummer extensions 1961 1961 1962 Offprint. (With J.-P. Serre & J. Tate) ‘A different with an odd class’, J. reine angew. Math. vol. 209 (1962), 6-7. Bibliog. no. 33 1962 C.21 C.22 C.23 C.24 C.25 C.26 A. Frohlich NCUACS 153/3/07 29 Publications, C.1-C.125 Photocopiedoffprint. ‘On non ramified extensions with prescribed Galois group’, Mathematika vol. 9 (1962), 133-134. Bibliog. no. 34 1962 Offprint. ‘Baer invariants of algebras’, Trans. Am. Math. Soc. vol. 109 (1963), 221-244. Bibliog. no. 35 1963 Offprint. ‘Galois algebras and their homomorphisms’, J. angew. Math. vol. 216 (1964), 1-11. Bibliog. no. 36 reine 1964 22pp manuscript draft, differently titled, headed ‘Original’; offprint. for modules separable ‘Invariants orders’, Q. J. Math. 2nd ser vol. 16 (1965), 193-232. Bibliog. no. 37 over commutative Offprint. ‘Some topics Oberwolfach Ber. vol. 2 (1966), 59-83. Bibliog. no. 38 of module conductors’, in the theory Offprint. This is an expanded version of Frdéhlich’s Oberwolfach lecture on module conductors. ‘Resolvents, discriminants, and trace invariants’, J. Algebra vol. 4 (1966), 173-198. Bibliog. no. 39 Offprint. ‘Radical modules over a Dedekind domain’, Nagoya Math. J. vol. 27 (1966), 642-662. Bibliog. no. 40 Offprint. 1965 1966 1966 1966 C.27 C.28 C.29 C.30 C.31 C.32 C.33 A. Frohlich NCUACS 153/3/07 30 Publications, C.1-C.125 C.34 C.35 C.36 ‘Quadratic forms “a la” local theory’, Proc. Camb. Phil. Soc. vol. 63 (1967), 579-586. Bibliog. no. 41 1967 Offprint. ‘Local fields’. In Algebraic Number Theory (Proc. 1965 Brighton conference). (ed. A. Frohlich and J.W.S. Cassels) London: Academic Press, 1967, 1-41). Bibliog. no. 42 1967 Offprint. (With J.V. Armitage) ‘Class numbers and unit signatures’, Mathematika vol. 14 (1967), 94-98. Bibliog. no. 43 1967 Offprint. C.36A ‘Homology of categories with quotients and K-theory’, not listed in Bibliog. 1967 Photocopied typescript paginated I-V, 1-57, dated ‘June 1967’. C.37 (With A.M. McEvett) ‘Forms over rings with involution’, J. Algebra vol. 12 (1969), 79-104; and ‘The representation of groups by automorphisms of forms’, JU. Algebra vol. 12 (1969), 114-133. Bibliog. nos. 44 and 45 1969 Offprints. C.38, C.39 Formal groups, Lecture Notes in Mathematics no. 74, Berlin: Springer, 1968. Bibliog. no. 46 1968 ‘Lecture notes of a course given London’, 1966-1967. at King’s College, C.38 C.39 ?Pre-publication bound copy Bound copy as published by Springer A. Frohlich NCUACS 153/3/07 C.40 C.41 C.42 C.43 C.44 31 1969 Publications, C.1-C.125 (With C.T.C. Wall) ‘Foundations of equivariant algebraic K- theory’. In Proceedings of Hull Conference (Lecture Notes 108) (ed. R.M.F. Moss and C.B. in Mathematics no. Thomas), pp. 12-27. Berlin: Springer, 1969. Bibliog. no. 47 Photocopied typescript. See also E.107. ‘Hermitian and quadratic forms over rings with involution’, Q. J. Math. Oxf. 2nd ser. vol 20 (1969), 297-317. Bibliog. no. 48 1969 Offprint. ‘On the classgroup of integral grouprings offinite Abelian groups’, Mathematika vol. 16 (1969), 143-152; and ‘On the classgroup of integral group rings of finite Abelian groups. I, Mathematika vol. 19 (1972), 51-56. Bibliog. nos. 49 and 54 1969, 1972 Offprints. ‘On the K-theory of unimodular forms over rings of algebraic integers’, Q. J. Math. Oxf. 2nd ser. vol 22 (1971), 401-423. Bibliog. no. 50 Offprint. (With C.T.C. Wall) ‘Equivariant Brauer groupsin algebraic number theory’, Bull. Soc. math. Fr. vol. 25 (1971), 91-96. Bibliog. no. 51 Offprint. See also C.45, C.45A, C.102, C.103, E.106-E.108. 1971 1971 C.45, C.45A (With C.T.C. Wall) ‘Generalisations of the Brauer group |’. Notlisted in Bibliog. ca 1971 The secondpart of this may be the draft at C.102, C.103. See also C.44, E.106-E.108. A. Frohlich NCUACS 153/3/07 32 Publications, C.1-C.125 C.45 53pp duplicated typescript C.45A Photocopied manuscript C.46 C.47 C.48 C.49 C.50 C.51 ‘Orthogonal and symplectic representations of groups’, Proc. Lond. Math. Soc. 3rd ser. vol. 24 (1972), 470-506. Bibliog. no. 52 Offprint. root numbers and ‘Artin bases for quaternion fields’, Invent. Math. vol. 17 (1972), 143-166. Bibliog. no. 53 normal integral Offprint. (With J. Queyrut) ‘On the functional equation of the Artin L- function for characters of real representations’, Inventiones math. 20 (1973), 125-138. Bibliog. no. 55 Offprint. ‘The Picard group of noncommutative rings, in particular of orders’, Trans. Am. Math. Soc. vol. 180 (1973), 1-45. Bibliog. no. 56 Offprint. ‘Artin root numbers, conductors and representations for generalised quaternion groups’, Proc. Lond. Math. Soc. vol. 28 (1974), 402-438. Bibliog. no. 57 Offprint. (With M. Keating and S.M.J. Wilson) ‘The classgroup of Quaternion and Dihedral 2-groups’, Mathematika vol. 21 (1974), 64-71. Bibliog. no. 58 Offprint. 1972 1972 1973 1973 1974 1974 A. Frohlich NCUACS153/3/07 33 Publications, C.1-C.125 See also E.119. ‘Module invariants and root numbers for quaternion fields of degree 4/’, Proc. Camb. Phil. Soc. vol. 76 (1974), 393- 399. Bibliog. no. 59 1974 Offprint. (With C.T.C. Wall) ‘Graded monoidal categories’, Compos. Math. vol. 28 (1974), 229-285. Bibliog. no. 60 1974 Offprint. See also E.109. ‘The Galois module structure of algebraic integer rings in fields with generalised quaternion group’, Bull. Soc. Math. Fr. vol. 27 (1974), 81-86. Bibliog. no. 61 Offprint. (With |. Reiner and S.V. Ullom) ‘Class groups and Picard groupsof orders’, Proc. Lond. Math. Soc. 3rd ser. vol. 29 (1974), 405-434. Bibliog. no. 62 Offprint. ‘Locally free modules over arithmetic orders’, angew. Math. vol. 274/275 (1975), 112-124. 63 J. reine Bibliog. no. Offprint. 1974 1974 1975 ‘Galois module structure and Artin L-functions’, Soc. Math. Fr. Astérisque vol. 24—25 (1975), 9-13. Bibliog. no. 64 1975 Offprint. ‘Artin root numbers for quaternion characters’, Symp. Math. vol. 15 (1975), 353-363. Bibliog. no. 65 1975 C.52 C.53 C.54 C.55 C.56 C.57 C.58 A. Frohlich NCUACS 153/3/07 34 Publications, C.1-C.125 Offprint. ‘Resolvents and trace form’, Math. Proc. Camb. Phil. Soc. vol. 78 (1975), 185-210. Bibliog. no. 66 1975 Offprint. ‘Module conductors and module resolvents’, Proc. Lond. Math. Soc. 3rd ser. vol. 32 (1976), 279-321. Bibliog. no. 67 1976 Offprint. ‘A normal integral basis theorem’, J. Algebra vol. 39 (1976), 131-137. Bibliog. no. 68 1976 Offprint. ‘Galois module structure and Artin L-functions’. In Proc.Int. Congress of Mathematicians, Vancouver, 1974 (ed. R.D. James) vol. 1, pp. 351-356. London: Academic Press, 1975. Bibliog. no. 69 Offprint. (With J.W.S. Cassels) ‘Hans Arnold Heilbronn 1908-1975’, Biogr. Mem.Fell. R. Soc. vol. 22 (1976), 119-135. Bibliog. no. 70 Offprint. The memoir was also reproduced in Bull. London Math. Soc. vol. 9 (1977), 219-232, an offprint of which (with a different photograph of Heilbronn) is also included. See also E.32-E.36. and ‘Arithmetic tame extensions’, J. reine angew. Math. vol. 286/287 (1976), 380-440. Bibliog. no. 71 structure Galois module for Offprint. 1975 1976 1976 C.59 C.60 C.61 C.62 C.63 C.64 A. Frohlich NCUACS 153/3/07 Publications, C.1-C.125 C.65 C.66 C.67 C.68 C.69 C.70 group In modules’. Hermitian ‘Local Conference on Quadratic Forms 1976 (Queen’s papers on pure and applied mathematics no. 46) (ed. G. Orzech), pp. 493-514. Kingston, Ontario: Queen’s University, 1977. Bibliog. no. 72 Photocopied (reduced size) typescript. ‘Galois module structure’ pp. 133-191 and ‘Stickelberger without Gauss sums’ pp. 589-707. In L-functions and Galois properties (Durham Proceedings 1975) (ed. A. Frohlich), London: Academic Press, 1977. Bibliog. nos. 74 and 75 Offprints. ‘Symplectic local constants and Hermitian Galois module structure’. In [International Symposium, Kyoto 1976(ed. S. lyanaga), for the Promotion of Science, 1977. Bibliog. no. 76 Tokyo: Japan Society 25-42. pp. Offprint. ‘Rings of integers in tame extensions as Galois modules’, Soc. Math. Fr. Astérisque vol. 41-42 (1977), 31-33. Bibliog. no. 77 Offprint. ‘Non-Abelian Jacobi sums’. In Number theory and algebra (ed. H. Zassenhaus), pp. 71-75. New York: Academic Press, 1977. Bibliog. no. 78 Offprint. ‘Some problems of Galois module structure for wild extensions’, Proc. Lond. Math. Soc. vol. 37 (1978), 193- 212. Bibliog. no. 79 Manuscript notes; offprint. 35 1977 1977 1977 1977 1977 1978 C.71 ‘On parity problems’ (Semin. Théorie des Nombres, 1979 A. Frohlich NCUACS 153/3/07 36 Publications, C.1-C.125 Bordeaux (1978-79) no. Bibliog. no. 80. 21). Talence: ONRS, 1979. 10pp typescript. (With M.J. Taylor) ‘The arithmetic theory of local Galois Gauss sums for tame characters’, Phil. Trans. R. Soc. Lond. A298 (1980), 141-181. Bibliog. no. 81 1980 Offprint. See also E.93. ‘Galois module structure and root numbers for quaternion extensions of degree 2”’, J. Number Theory vol. 12 (1980), 499-518. Bibliog. no. 82 Offprint. ‘The Hermitian classgroup’. In Integral representations and applications, in mathematics no. 882) (ed. K.\W. Roggenkamp), pp. 191— 206. Berlin: Springer, 1981. Bibliog. no. 83 Oberwolfach notes 1980 (Lecture Photocopied typescript. ‘Algebraic number theory’. In Emmy Noether, a tribute to herlife and work (ed. J. Brewer and M. Smith), pp. 157- 163. New York: Marcel Dekker, 1981. Bibliog. no. 84 11pp typescript; offprint. ‘Value distributions of symplectic root numbers’, Proc. Lond. Math. Soc. 3rd ser. vol. 46 (1983), 83-99. Bibliog. no. 85 35pp typescript draft; offprint. 1980 1981 1981 1983 ‘Galois module structure of algebraic integers’, Springer Ergebn. 3rd ser. vol. 1 (1983), 1-258. Bibliog. no. 86 1975-1986 Correspondence re Frohlich’s contribution, 1975-1980; C.72 C.73 C.74 C.75 C.76 C.77 A. Frohlich NCUACS 153/3/07 37 Publications, C.1-C.125 reviews, 1985, 1986. (With C.J. Bushnell) Gauss sums and p-adic division algebras (Lecture notes in mathematics no. 987). Berlin: Springer, 1983. Bibliog. no. 87 1983 These lectures were delivered at the UniversityofIllinois in autumn 1981, when Frohlich was G.A. Miller Visiting Professor there. See also D.7. Bound voiume. Central Extensions, Galois Groups and Ideal Class Groups of NumberFields, Contemp. Math. vol. 24 (1983). Bibliog. no. 88 Bound volume, with flyer from American Mathematical Society enclosed. ‘Class groups and Hermitian Modules’, Prog. Math. vol. 48 (1984), 1-226. Bibliog. no. 89 Bound volume. C.78 C.79 C.80 1983 1984 1983 1984 C.81, C.82 Gauss’sche Summen. Notes of lectures taken by Kleinert, Denninger, Everest. 2 vols. Mathematische Institut Koln, 1983. Bibliog. no. 90 Notes on lectures delivered in Koln 1982 (see D.11) and Cambridge 1983. Bound volumes. 2 folders. C.83 ‘Gauss sums’. In Sémin. Théorie des nombres, Paris, 1982-83 (Progr. (ed. M-J. Bertin and C. Goldstein), pp. 91-101. Boston, MA: Birkhauser, 1984. Bibliog. no. 91. Math. 51) Manuscript and typescript drafts; offprint. C.84 (With C.J. Bushnell) ‘Non-Abelian congruence Gauss sums 1985 A. Frohlich NCUACS 153/3/07 Publications, C.1-C.125 and p-adic simple algebras’, Proc. Lond. Math. Soc. 3rd ser. vol. 50 (1985), 207-264. Bibliog. no. 93 Offprint. C.85 C.86 C.87 C.88 C.89 ‘Orthogonal representations of Galois groups, Whitney classes and Hasse—Witt invariants’, angew. Math. vol. 360 (1985), 84-123. Bibliog. no. 94 J. Stiefel— reine Offprint. See also E.1. ‘Principal orders and embedding oflocal fields in algebras’, Proc. Lond. Math. Soc. 3rd ser. vol. 54 (1987), 247-266. Bibliog. no. 95 Offprint. Tame representations of local principal orders, local Weil orders, groups and chain groups of local der Sitzungsberichte Heidelberger der Wissenschaften Mathematische-naturwissenschaftliche Klasse 1986, Berlin: Springer, 1986. Bibliog. no. 96 principal Akademie Bound volume. See also C.90. ‘Problems in representation theory arising from Galois modules (Arcata 1986)’. Proc. Symp. Pure Maths vol. 47 (1987), 81-85. Bibliog. no. 97 Offprint. ‘L-functions at S=0 and Galois modules’. In Semin. Théorie des Nombres, Bordeaux (1986-87), no. 32 (1987), 1-20. Bibliog. no. 98 Offprint. See also D.24. 38 1985 1987 1986 1987 1987 A. Frohlich NCUACS 153/3/07 39 Publications, C.1-C.125 C.90 C.91 C.92 C.93 C.94 C.95 ‘Tame representation in base change’, Contemp. Math.vol. 86 (1989), 207-213. Bibliog. no. 99 1989 This was a shorter version of Bibliog. no. 96 (C.87). Offprint. ‘The papers on discriminants of cubic fields’. In Collected papers of Hans Arnold Heilbronn (ed. E.J. Kani and R.A. Smith), pp. 292-297. Toronto: Wiley-Interscience, 1986. Bibliog. no. 100 1986 Proof; photocopiedarticle. ‘Module defect and factorisability’, //linois J. Math. vol. 32 (1988), 407-421. Bibliog. no. 101 1988 Offprint. Untitled draft beginning ‘Let K be a numberfield L a finite Galois extension of K’. Notlisted in Bibliog. ca 1988 39pp typescript ‘L-values at zero and multiplicative Galois module structure (also Galois Gauss sums and additive Galois module structure)’, J. reine angew. Math. vol. 397 (1989), 42-99. . Bibliog. no. 102 1989 Offprint. ‘The genus class group |’, Sémin. Théorie des Nombres, Bordeauxvol. 4 (1992), 97-111. Bibliog. no. 103 1992 Photocopiedoffprint. C.96, C.97 (With M.J. Taylor) Algebraic number theory. Cambridge University Press, 1991. Bibliog. no. 104 1991, 1995 C.96 Copyof book. . 1991 A. Frohlich NCUACS153/3/07 C.97 C.98 Publications, C.1-C.125 Review ‘Units in real Abelian fields’, J. reine angew. Math. vol. 429 (1992), 191-217. Bibliog. no. 105 ‘Omitted proofs’ (retained in original folder); offprint. 40 1995 1992 C.99-C.104 ‘Strict factorisability and shadows’. In Algebra and Number Theory, Essen 1992 (ed. G. Frey and J. Ritter), pp. 1-25. Berlin: de Gruyter, 1994. Bibliog. no. 107 1994, 1997 C.99 39pp typescript draft C.100 C.101 ‘Corrected final’ draft, 23pp typescript Photocopied manuscript and typescript pages in Frohlich’s hand beginning ‘2 The class of a principal factorisation’; typescript note ‘2 The class of a principal factorisation’, with note from ‘Jurgen [Ritter]’ attached, ‘Lieber Ali, ist das das Richtige?’, 16 April 1997; photocopied manuscript pages. 1994 1994 1997 C.102, C.103 ‘Il. Equivariant classgroups and Brauer groups’ N.d. 61pp manuscript working, found with preceding material but appears to be earlier in date. This may be related to ‘Generalisations of the Brauer group I’ (see C.45, C.45A). 2 folders. See also C.44, C.110, E.106-E.111. C.104 workings Manuscript connection with the factorizability [...]’ ‘These regulator are defined computations in by AF and N.d. C.105-C.108 ‘Galois modules and the functional equation’. Bibliog. Notlisted in ca 1995 A. Frdhlich NCUACS153/3/07 41 Publications, C.1-C.125 C.105 Manuscript and photocopied manuscript sections C.106-C.108 Typescript drafts, three (slightly) different versions 3 folders. C.109 C.110 ‘Some remarks on wild extensions of number fields’, J. reine angew. Math. vol. 495 (1998), 29-33. Bibliog. no. 108 1998 8pp photocopied manuscript draft; offprint. (With C.T.C. Wall) ‘Equivariant Brauer groups’, Contemp. Math. vol. 272 (2000), 57-71. Bibliog. no. 109 ~ 2000 Qpp typescript; offprint. See also C.44, C.45, C.102, C.103, E.106-E.111. C.111 ‘On the unit group normal numberfields’ App typescript. C.112-C.116 Incomplete draft of ?book on ‘mathematical theory of ostensive and consequently of empirical predicates’ 5 folders. N.d. N.d. C.117-C.119 Draft beginning ‘Chapter 2 The cohomology theory E//*(X)’ N.d. 3 folders. C.120 ‘Ali Frohlich’s review of Hassé Collected works’ 5pp typescript so headed. C.121, €.122 Draft on groupoid spaces N.d. N.d. A. Frohlich NCUACS 153/3/07 Publications, C.1-C.125 43pp duplicated typescript. 2 folders. C.123 C.124 Review of Les conjectures de Stark sur les fonctions L d'Artin en s=0: notes d'un cours a Orsay [de] John Tate by D. Bernardi and N. Schappacher, Boston, 1984 Referee’s ‘Report on “Units in Real Abelian Fields”, by A. Frohlich’ 7pp typescript; comments on Fréhlich’s report. 42 1984 1991 C.125 Refereeing 1975, 1983, n.d. A. Frohlich NCUACS 153/3/07 SECTION D VISITS, CONFERENCES AND LECTURES, D.1-D.43 43 1956-1998, n.d. D.1 ‘A reciprocity relation between pairs of quadratic forms’, lecture given in Vienna, Austria, September 1956 1956 6pp typescript resume. D.2 Visit to California, USA 1961, 1962 Frohlich was visiting as Senior Research Fellow in Mathematics, California Institute of Technology, Pasadena, January-June 1962. See also E.83. Invitation; UCLA weekly calendar for 18-25 March 1962 (Frohlich is listed as leading a Mathematics Colloquium on ‘Discriminants of algebraic number fields’, 22 March); California Institute of Technology weekly calendar for 30 April-6 May (Frohlich is listed as lecturing on ‘Inverse problem of Galois theory’, 1 May). D.3 Visit to University of Arizona, January-June 1971 1971 Photocopy of newspaper cutting visiting as National Science Foundation Fellow. referring to Frdhlich D.4 Research Symposium on Algebraic Number Theory, UK, 2- 12 September 1975 1975 List of participants receiving Science Research Council support. D.5 Visit to Israel, September-December 1978 1978 Frohlich was Royal Research Professor. Society-lsrael Academy Visiting Letter from Royal Society re financial arrangements. D.6 Retirement Seminar, King’s College London, 12 June 1981 1981 Programme. A. Frohlich NCUACS 153/3/07 44 Visits, conferences and lectures, D.1-D.43 D.7 Visit to University ofIllinois at Urbana-Champaign, 1981- 1982 1981 as a Miller Frohlich was visiting the Department of Mathematics. For the academic year 1981- 1982 the University hosted a year-long programme in Algebraic Number Theory and Algebra, with a numberof other eminentvisiting scholars. Professor in lectures on Algebraic Announcement; programme for Number Theory and Algebra (Frohlichis listed as lecturing on ‘Galois module structure and the embedding problem’); invitation to lecture at University of Chicago in February 1982 (invitation annotated by Frohlich ‘Normal bases - History and recent progress’). See C.78 for published lectures. Colloquium marking the Centenary of the birth of Emmy Noether (1882-1935), University of Erlangen-Nurnberg, Germany, 27 February 1982. 1982 Frohlich Zahlentheorie’. lectured on ‘Emmy Noethers Beitrag zur Programme,invitation and correspondencearising. American Mathematical Society 793rd Meeting, Bryn Mawr College, Pennsylvania, USA, 16-17 March 1982 1981, 1982 Frohlich lectured on ‘Rings of algebraic integers as Galois modules’. Invitation, programme, photocopied manuscript lecture notes. Colloquium on Number Theory, Luminy, France, 28-June-3 July 1982 1981 Invitation from G. Henniart, annotated ‘Value distributions of root numbers and free Galois modules’. to Germany, 6 June-30 July and 24 October-4 Visit December 1982 1982 Frohlich was based at the University of KdIn. D.8 D.9 D.10 D.11 A. Frohlich NCUACS 153/3/07 45 Visits, conferences and lectures, D.1-D.43 Notice of three lectures at Kéln, ‘Gauf’sche Summen und Galois Modul Struktur, Gauf’sche Summen und lokale Langlands-Theorie’ and ‘The arithmetic theory of local of GauR sums Heidelberger of Heidelberg, 9 July (Frohlich is lecturing on Gauf&§sche Summen fur einfache Algebren’); notice of lecture by Frohlich on ‘GauRsche Summen’, University of Augsburg, 12 November. for Zahlentheorie programme University Kolloquium, characters’; tame The Kéln lectures were published as Gauss’sche Summen. Notes of lectures taken by Kleinert, Denninger, Everest. 2 vols. Mathematische Institut KélIn, 1983 (see C.81,C.82). D.12 Shorter correspondencerevisits and conferences 1983 1982-1983 Conference at Oberwolfach, 10-16 April 1983; invitation to visit the University of Bordeaux |, in the year 1983-1984; letter re Conference on Quadratic forms and Hermitian K- theory, McMaster University, Hamilton, Ontario, Canada. D.13 D.14 Conference on Mathematisches Germany, 3-9 June 1984 Orders Forschungsinstitut, and_ their Applications, Oberwolfach, 1984 Programme. Frohlich lectured on ‘Principal orders and arithmetic’. Conference Mathematisches Germany, 5-11 August 1984 on Algebraische Forschungsinstitut, Zahlentheorie, Oberwolfach, 1984 Programme, abstracts. Frohlich lectured ‘On Serre’s formula for the trace form’. D.15 Visit to The Netherlands, December 1984 1984 Letter to J. Brinkhuis re schedule; programme of meeting at the Erasmus University, 10 December (Frohlich is listed as lecturing on ‘Gauss sums for tame representation of local Weil-Deligne groups and oflocal principal orders’). Rotterdam, A. Frohlich NCUACS 153/3/07 46 Visits, conferences and lectures, D.1-D.43 D.16 D.17 American Mathematical Society 818th Meeting, University of Arizona, Tucson, USA, 12-13 April 1985 1985 Annotated programme. Mathematics Germany, 14 June 1985 Colloquium, Programme. University of Augsburg, 1985 Frohlich lectured on ‘Multiplikative und additive Galois- Modul-Struktur’. D.18 Pure Mathematics Workshop on Galois Modules and Zeta Functions’, University of Exeter, 2-6 September 1985 1985 Letter from participants; programme. R.W.K. Odoni re arrangements; list of Frohlich lectured on ‘Wild Galois module structure and Gauss sums’. Number Theory Seminar, October 1985 Programme. King’s College London, 16 1985 Frohlich lectured on ‘Galois module structure of units’. Conference on Representation Theory and Number Theory in Conjecture’, University of Augsburg, Germany, 8-14 December 1985 connection Langlands local with the 1985 D.19 D.20 Programme and arrangements. Frohlich lectured on ‘Tame Deligne representations of Weil groups, principal orders and base change’. D.21 Colloquium to mark the 65th birthday of Herbert Benz, University of Koln, 25 January 1986 1986 Programme. Frohlich Summen und Langlands’sche Vermutung’. ‘Hauptordnungen, lectured on Gauf’sche A. Frohlich NCUACS 153/3/07 D.22 Visits, conferences and lectures, D.1-D.43 on Arithmetic Meeting of Manchester Institute of Science and Technology, 20-21 June 1986 University module, Galois 47 1986 Programme. Frohlich gave lectures on ‘Galois module structure |’ and ‘Galois module structureII’. D.23 Shorter correspondence re visits and conferences 1986- 1987 1985 Society Mathematical American Summer Research Institute on Representation Theory of Finite Groups and Related Topics, University of California at Berkeley, 6-25 July Mathematical Sciences Research Institute, Berkeley, California, 1986-1987. 1986; visit to D.24 Seminar on Number Theory, University of Bordeaux I, June 1987 1987 Invitation; ‘Calculations and corrections in connection with 1987 Bordeaux paper’; copy of lecture as published. lectured on ‘L-functions Frohlich modules’. Published in Semin. Bordeaux (1986-87), no. 32 (see also C.89). at S=0 and Galois Théorie des Nombres, D.25 Visit to China, autumn 1987 1987 Frohlich was Visiting Professor at the University of Beijing. Letter re arrangements. D.26 Shorter correspondencerevisits and conferences 1988 1987, 1988 of Galois modules organised by Meeting on arithmetic University and Technology, 17-20 April 1988; NATO Advanced Studies Institute Banff, Canada, 27 April-5 May 1988. in Number Theory and Applications, Manchester Science Institute of A. Frohlich NCUACS 153/3/07 48 Visits, conferences and lectures, D.1-D.43 D.27, D.28 Visits to Germany, summer 1988 1987, 1988 D.27 Conferences Oberwolfach at Mathematisches Forschungsinstitut, 1987, 1988 D.28 D.29 D.30 Orders and their Applications, 29 May-4 June (Frohlich lectured on ‘Factorvariability of group modules’) and Algebraische Zahlentheorie, 7-13 August (Frohlich lectured on ‘Multiplicative Galois module structure’). Invitations, programmes. Meeting on Galois theory of local and global numberfields, Gottingen, 6-10 June (Frdhlich gave two lectures on ‘Multiplicative Galois module structure and L-values at s=0’) Handbook of abstracts; photocopied manuscript notes. London Mathematical Society meeting on Arithmetic Galois Modules, University of ManchesterInstitute of Science and Technology, 23-24 February 1989 Programme, report Mathematical Society. by Frohlich for the London Frohlich lectured on ‘Genus Class-groups Factorizability and Galois module structure’. 1988 1989 London Mathematical Society symposium on L-functions and Arithmetic, University of Durham, 30 June-11 July 1989 1989 List of participants; annotated programme. Frohlich lectured on the theme of L-functions and Galois modules. D.31 Shorter correspondencere visits and conferences 1989 1989 Invitation to visit and lecture at University of lowa, USA, between August 1989 and May 1990, annotated by Frohlich London Mathematical Society re financial support for meeting on Arithmetic Galois Modules, Cambridge, September. ‘March, April [...]; letter from A. Frohlich NCUACS 153/3/07 49 Visits, conferences and lectures, D.1-D.43 D.32 Colloquium at University of Augsburg, Germany, 24-25 November 1989 1989 Invitation; programme. Frohlich lectured zahlentheoretische analytischer Methoden’. on Andwendung~ ‘Galoismodulstruktur —- algebraischer eine und D.33 Visit to McMaster University, Hamilton, Ontario, Canada, March 1990 1989, 1990 Invitation; list of Mathematics and Statistics Department activities listed as lecturing on ‘Units in Abelian fields’ and giving a colloquium on ‘Arithmetic Galois modules’). for 19-23 March 1990 (Froéhlich is D.34 D.35 D.36 D.37 Visit to Eidgendéssiche Technische Hochschule, Zurich, Switzerland, June 1990 1989, 1990 Invitation and letter re arrangements; letter re visit to ?University of KdIn, June 1989. Colloquium on Structures University September 1990. Bordeaux of |, Galoisiennes Arithmetiques, 24-28 Talence, France, 1990 Outline of subjects to be covered (in French). Galois Isaac University of Cambridge, 27 April 1993 Workshop, Module Newton Institute, 1993 Programme. Frohlich lectured on ‘Shadows and L-functions’. Conference on Integral Galois Structures, University of Augsburg, Germany, 18-23 July 1993 1993 Bound conference report. Frohlich structure’. lectured on ‘Strict factorisability in additive A. Frohlich NCUACS 153/3/07 Visits, conferences and lectures, D.1-D.43 D.38 D.39 Conference on Mathematisches Germany, 16-22 April 1995 Orders in Forschungsinstitut, Arithmetic and Geometry, Oberwolfach, Conference handbook. Frohlich lectured on ‘Galois Gauss sums and factorization’. Conference on Mathematisches Germany, 17-23 January 1999 Orders in Forschungsinstitut, Arithmetic and Geometry, Oberwolfach, 50 1995 1998 Invitation and booking form; 11pp photocopied manuscript lecture notes. Frohlich lectured ‘On wild extensions of number fields’. D.40 Programme for unidentified two week meeting N.d. Frohlich is listed as lecturing on ‘Hermitian structure of algebraic integers’. D.41 Contents of folder inscribed ‘Lecture’. Transparencies for lecture ?0n numbertheory. D.42 D.43 Manuscript notes labelled ‘Talks. Manitropic: factorizibility (but also topics from the Springer and Birkhauser book)’. Manuscript draft of lecture beginning ‘A few years ago | discussed some new invariants of a discriminantal type — | have called them module conductors’. N.d. N.d. N.d. A. Frohlich NCUACS 153/3/07 51 SECTION E CORRESPONDENCE, E.1-E.125 1950-2000 section is surviving Frohlich’s This mathematical correspondence. A number of the major sequences of correspondence with individuals were kept together with treasury tags or staples but there is evidence that some letters were later removed by Frohlich, and while many were then found loose or in shorter sequences, a number were not found. The section is arranged in an alphabetical sequence. It is international in scope, with many correspondents from North America, France and Germany. Many of the letters focus on progress of research and include discussions of mathematical workings, sometimes as problems with separate documents, and drafts of papers. Although it spans 1950-2000, the bulk dates from the 1970s-1990s. E.1 Adams, J.F. Comments on draft of appendix | to Frohlich’s ‘Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse—Witt invariants’, J. reine angew. Math. vol. 360 (1985). See C.85. E.2 Bayer, E. Bayer was based at the University of Geneva. Includes photocopied manuscript draft ‘Isometric structures with an irreducible characteristic polynomal’ by Bayer. 1984 1979 E.3 Berge, A.-M. 1976-1980 Berge was based at the U.E.R. de Mathematiques et d'Informatique, University of Bordeaux |, Talence, France. Includes manuscript draft of ‘Local Galois module structure in the wild case’ by Berge. E.4-E.7 Brinkhuis, J. 1984-2000 Brinkhuis was based at Rotterdam, The Netherlands. the Erasmus University of A. Frohlich NCUACS 153/3/07 52 Correspondence, E.1-E.125 Chiefly draft papers sent to Frohlich for comment. Includes typescript draft ‘Relative Galois module structure for quartic fields’ 1984, 1988 Includes typescript draft ‘On a comparison of Gauss sums with products of Lagrange resolvents’ ca 1989 Includes photocopied manuscript draft ‘Normal integral bases and the Spiegelungssatz of Scholz’ 1990 Includes fragmentsofletters 2000, n.d. E.4 E.5 E.6 E.7 E.8 Burns, D. Typescript drafts sent to Frohlich: ‘Adams operations and integral Galois representations’, ‘On twisted Galois-Gauss sums and canonical factorizations’, arithmetically realisable ‘A remark concerning arithmetical associated orders’. classes’, ‘On 1992, 1993, n.d. 1980s-1996, n.d. E.9-E.14 Bushnell, C.J. Bushnell was a postgraduate student of Frohlich’s at King’s College London 1968-1971 (Ph.D. ‘Representations of 23- Graded Groups’, see F.12). He was appointed Temporary Lecturer at King’s in 1971 and after a period at the University ofIllinois 1972-1974 returned to King’s in 1974, being appointed Professor of Pure Mathematics in 1990. CVs, research statements etc. 1980s, 1990s Correspondence Chiefly re career, progress of research. orders, supercuspidal ‘Hereditary representations of GLy [...] To Albrecht Fréhlich on his seventieth birthday’, 54pp typescript. Gauss sums and_ 1984, 1985, n.d. 1986 E.9 E.10 E.11 A. Frohlich NCUACS 153/3/07 53 Correspondence, E.1-E.125 E.12 Correspondence 1987, 1988 Includes photocopied manuscript draft ‘Conductors of primitive by Bushnell sent to Frohlich for comment. representations’ Galois E.13 E.14 E.15 E.16 E.17 for GL (N)’ Letter on work in progress, with typescript drafts of ‘Local tame lifting ‘Smooth representations of p-adic groups: the role of compact open subgroups’ and ‘Smooth representations of reductive p- adic groups’, with P.C. Kutzko. Henniart, with G. 1995 Citation for Bushnell; undated letter from Frohlich 1996, n.d. 1972-1990 1966-1975 N.d. Cassels, J.W.S. Cassou-Nogués, P. Cassou-Nogués wasbased at U.E.R. de Mathématiqueset d’Informatique, University of Bordeaux |, Talence, France. Chiefly on work in progress, with mathematical workings. Although the letters are dated with the day and month, they do not bear the year so cannot be placed in chronological order. E.17A Chase, S.U. 1977 62pp manuscript on the local theory of resolvent and related invariants. E.18 Chinburg, T.C. 1985-1989, n.d. Chinburg was Assistant Professor, then full Professor of Mathematics at the University of Pennsylvania. Career, work in progress. A. Frohlich NCUACS 153/3/07 54 Correspondence, E.1-E.125 E.19 Cougnard, J. Cougnard was based at the University of Franche-Comté, Besancon, France. Includes ‘Bourbaki talk’. correspondence 1981-1982 re Cougnard’s Cougnard’s letters are in French. E.20 E.21 E.22 C. D.-E. Erez, B. Includes Erez’s ‘Abstract of past research and research plans for 1990’ and outlines of planned book on ‘Galois modules in arithmetic’, with Frohlich’s responses. 1978-1982, n.d. 1983, n.d. 1963-1988 1990-1993, 1999 E.23. F. E.24 Galovich, S.P. the time Galovich was Professor At Mathematics at Carleton College, Northfield, Minnesota. writing of 1967-2000 1972-1973 of Includes correspondence re projective class group. Galovich’s work on the E.25 E.26 Garbanati, D. Geyer, W.-D. 1975-1976 1980 Collected works of H. Hasse. Includes 5pp draft typescript of introduction. A. Frohlich NCUACS 153/3/07 55 Correspondence, E.1-E.125 E.27 Gras, G. 1973-1974 Progressof research. Gras’s letters are in French. E.28 Green, J.A. Correspondence 1964 re problem from number theory. E.29 E.30 Hall, P. Hall was Sadlerian Professor of Pure Mathematics at Cambridge. 1964, 1968, 1987 1968-1994 1958-1965 E.31 Hasse, H. 1965, 1974 Hasse was Professor of Mathematics at the University of Hamburg. Incoming letters only. In German. Correspondence 1965 is chiefly re arrangementsforvisit to London. E.32-E.36 Heilbronn, H.A. 1950-1976 Heilbronn had fled Germany in 1933. He was appointed Reader in Mathematics at the University of Bristol in 1946 and Professor and Head of the Department 1949. He moved to Canada in 1964 where he was appointed to a chair of mathematics at Toronto University. Heilbronn was Frohlich’s Bristol. Frohlich and J.W.S. Cassels wrote the Royal Society Biographical Memoir of Heilbronn (see C.63). supervisor at Ph.D. E.32 Correspondence and papers 1950-1955 Research in progress, social news(all incoming). Correspondence of August 1955 includes manuscript workings. A. Frohlich NCUACS 153/3/07 Correspondence, E.1-E.125 56 1957, 1959 E.33 E.34 E.35 E.36 including Correspondence criticism of paper by Frohlich to be submitted to the London Mathematical Society. progress, research re in Correspondencere research in progress, including Abelian fields and Artin L-functions. 1970 Correspondencere researchin progress, including Artin L- functions, and possible visit of Heilbronn to London as a Visiting Fellow. 1972-1974 Correspondence and papers re Biographical Memoir of Heilbronn. Including drafts of sections of the Memoir. 1975-1976 Includes contributions from C.A. Rogers, P. Du Val and R. Rado, H.S.M. Coxeter and T. Callahan. E.37 Holland, D. 1991-1993 Correspondence re move to McMaster University, Canada; draft papers on Chinburg’s Third Invariant. E.38 Hsia, J.S. 1970 Hsia was Professor University, USA. of Mathematics at Ohio State Correspondencere problems of Ker A and Ker 2. E.39 E.40 Kani, E. Kani was based at Harvard University. 1966-1989 1983-1988 Correspondence Heilbronn’s collected works. re preparation of volume of HA. A. Frohlich NCUACS 153/3/07 57 Correspondence, E.1-E.125 E.41 Kawamoto, F. 1983, 1984 Kawamoto was Gakushuin University, Japan. a_ postgraduate student based at includes ‘On normal integral bases of local fields’ by Kawamoto sent to Frohlich for comment. E.42 Kneser, M. 1964-1985 Kneser was based at Géttingen, Germany. the Georg-August Univeristy, Later correspondence(chiefly incoming) in German. Includes correspondence re possible visit to Géttingen as Guest Professor (1982-1983), and progress of research. E.43 Knus, M.A. 1970-1985 Knus was based Hochschule, Zurich, Switzerland. the at Eidgendéssiche Technische Progress of research. E.44 Koch, H. 1965-1989, n.d. Koch was based Wissenschaften zu Wissenschaften der DDR), East Berlin, East Germany. Deutsche Akademie der (later the Akademie der at the Berlin Progress of research, visits. E.45 Kuroda, S.-N. 1954-1974 Progressof research, visit to London 1968-1969. E.46 E.47 Lecouturier, P. Lecouturier was a Belgian mathematician. Research on epimorphism. 1967-1996 1965, 1966 A. Frohlich NCUACS 153/3/07 E.48 E.49 Correspondence, E.1-E.125 McCulloh, L.R. McCulloh was Professor of Mathematics at University of illinois at Urbana-Champaign. Chiefly re progress of research. 58 1966-1988 1978-1985, n.d. E.50 Macdonald, |.G. 1986 Correspondence re working ‘Let O € Gal (Q cycl/Q)’. E.51 McEvett, A.W. 1969, 1970 McEvett was a postgraduate student of Frohlich’s at King’s College London in the 1960s (Ph.D. ‘Hermitian Forms over Algebras’, see F.8). Correspondence re working ‘Let [ be an infinite group of order n and let K be a field whose characteristic does not divide 2 or n’ (1969) and paper ‘On the splitting by subalgebras of algebras with involution traces’ (1970). E.52-E.54 Martinet, J. 1970-1992 E.52 E:53 E.54 Martinet was based at the U.E.R. de Mathématiques et d'Informatique, University of Bordeaux |, Talence, France. Curriculum vitae Correspondence re progress of research including paper on W(x)=1, visits of Martinet and J. Queyrut to London and Frohlich to Bordeaux 1992 1970-1974 Correspondence re progress of research including the problem of notation for root numbers and Gauss sums, and examining the thesis of P. Cassou-Nogués(see F.25) 1975-1984 A. Frohlich NCUACS 153/3/07 Correspondence, E.1-E.125 E.55 Milnor,J. Correspondence and papers re W(D), including manuscript workings by Frohlich. 59 1971 E.56 Narkiewicz, W. 1964-1979 Narkiewicz was based at the Poland. University of Wroclaw, Includes answers. questions on normal fields, with Frdhlich’s E.57 Nelson, A.M. 1981, 1984 Nelson was a postgraduate student of Frohlich’s at King’s College London in ‘Monomial Representations and Galois Module Structure’, see F.18). He then moved to Macquarie University, Australia. late 1970s (Ph.D. the E.58 Ojanguren, M. 1972 Ojanguren was based at the Battelle Advanced Studies Centre, Geneva, Switzerland. Correspondence re work on Azumaya algebras. E.59 E.60 E.61 E.62 O. Perlis, R. Perlis was Professor of Mathematics at the Louisiana State University, Baton Rouge, USA. Includes a manuscript working by Perlis on the zeta function. Rédei, L. Rédei was based at the Bolyai Mathematical Institute, 1979-1993 1983-1984 1972-1980 1954-1960 A. Fréhlich NCUACS 153/3/07 60 Correspondence, E.1-E.125 Szeged, Hungary. Progressof research. Incoming correspondenceonly, in German. E.63, E.64 Reiner, I. 1971-1983 Reiner was based at the University ofIllinois at Urbana- Champaign. Includes joint correspondence to Reiner and S.V. Ullom (see also E.99-E.104). Reiner, Ullom and Frohlich co- authored ‘Class groups and Picard groupsof orders’, Proc. Lond. Math. Soc. 3rd ser. vol. 29 (1974) (see C.55). E.63 Correspondence and paperschiefly re work in progress on Picent (A) — (C) and Picard groups, including comments on drafts. 1971-1972 E.64 Correspondence E.65, E.66 Ritter, J. For most of the period covered by the correspondence Ritter was based at the University of Augsburg, Germany. Most of the correspondenceis in German. 1979, 1981, 1983 1980-1994 1980-1990 E.65 E.66 E.67 Correspondence and papers, including manuscript and photocopied manuscript workings by Frohlich, and text of talk group representations’ by Ritter, referring to Fréhlich’s work on Galois module structure integrality ‘On the by Ritter on of Correspondence onprogressof research 1991-1994 Rocquette, P. 1975-1992 Rocquette was Professor of Mathematics at the University of Heidelberg, Germany. A. Frohlich NCUACS 153/3/07 61 Correspondence, E.1-E.125 Includes correspondence re progress of research and re organisation of the Oberwolfach meetings for 1982 and 1986. Mostof the correspondenceis in German. E.68 Rosenberg, A. 1971 Correspondencere research problem. E.69 E.70 Schertz, R. Schertz was a mathematician based in Kd6In, Germany. Mostof the correspondenceis in German. 1965-1996 1978-1981 E.71-E.77 Serre, J.-P. 1960-1986 Serre, one of the leading mathematicians of the twentieth century (winning the Fields Medal at the age of 28), was Professor of Algebra and Geometry at the Collége de France, Paris. Much of the incoming correspondenceis in French. Correspondence, including invitation to Serre to participate in London Mathematical Society 1965 summer school on algebraic number theory, and correspondencere areas to be covered 1960-1965 Correspondence re work in progress, including Serre’s comments on article by Frohlich and J.V. Armitage, ‘Class numbers and unit signatures’, Mathematika vol. 14 (1967) (see C.36) 1966-1971 Correspondence including re ‘problem of the root number and normal integral basis of a field N with quaternion Galois group over Q’, and proof of w(x)= +1 1972 E.71 E.72 E.73 A. Frohlich NCUACS 153/3/07 62 E.74 E.75 E.76 E.77 E.78 Correspondence, E.1-E.125 Correspondence re work in progress including Serre’s comments on draft of Artin root numbers, conductors and representations for generalised quaternion groups’, Proc. Lond. Math. Soc. vol. 28 (1974) (see C.50), and Galois modules 1973-1974 and progress, Correspondence in_ Includes attendance at meetings, visit to London etc. photocopied manuscript workings by Serre, ‘Tate or “Stark” (1978) and ‘La formule de Frohlich’ re work papers 1975-1978 Correspondence re work in progress, including Serre’s comments on chapters 1-3 of Froéhlich’s draft of ‘Galois module structure of algebraic integers’ (see C.77) 1979-1981 Correspondence re workin progress 1982-1986 Snaith, V. 1984-1986 Snaith was based at the University of Western Ontario, London, Canada. Includes correspondence re differences in approaches, (with Snaith’s manuscript ‘Comments on “The equivariant SW, ...representation” the University of Western Ontario, 1986. invitation ’) and to visit E.79 Strooker, J.R. 1967-1971 Strooker was based at the University of Utrecht. E.80 E.81 S. Tate, J.T. 1966-1980, n.d. 1964-1976 Tate was Professor of Mathematics at Harvard University. re arrangements for Chiefly including London Mathematical Society 1965 summer school on algebraic number theory. visits, A. Frohlich NCUACS 153/3/07 Correspondence, E.1-E.125 E.82-E.90 Taussky-Todd, O. 63 1957-1987, n.d. Olga Tausskyfled the Nazis in 1934 and came to the UK. After the war she and her husband John Todd, also a mathematician, moved to the USA. In 1957 they both joined the California Institute of Technology, Pasadena. She was made Professor in 1971. Taussky-Todd was Frohlich’s external examiner for his Ph.D. Frdhlich was writing the obituary of Taussky-Todd for the London Mathematical Society. Correspondence re quadratic subfields with quaternions Galois group and other work in progress, and visits of fields 1957-1960 Frohlich’s planned visit in 1958 was cancelled as he was unable to get an American visa. California Correspondence re visit Institute Fellow of Technology January-June 1962, work in progress on ideal matrices and algebraic numbertheory of Frohlich as to the Senior Research 1961-1965 See also D.2. Correspondence re work in progress, planned visit to California Institute of Technology 1968 1966-1971 Correspondence re work in progress, including symmetry and group rings, possible visits 1972-1973 Correspondence re workin progress, visits and conference attendance, including lecture by Taussky-Todd at King’s College on ‘Some facts concerning integral matrices’, December 1974 1974-1975 Correspondence chiefly re visits, news of colleagues, research plans 1976-1978 Correspondence re work on numbertheory and other work 1979-1981 E.82 E.83 E.84 E.85 E.86 E.87 E.88 A. Frohlich NCUACS153/3/07 64 Correspondence, E.1-E.125 in progress, visits, news of colleagues E.89 Correspondence and papers Includes photocopied manuscript note beginning, ‘There is of course a large body of theory on orders in algebras over number fields and over local fields’, undated. E.90 re obituary Letter London Mathematical Society, copy of obituary in Notices of the American Mathematical Society, August 1996, manuscript notes by Frdhlich Taussky-Todd for of 1984, 1987, n.d. 1996 E.91-E.97 Taylor, M.J. 1977-2000 London 1973-1976 Taylor was a postgraduate student of Frohlich’s at King’s College Module Structure of the Rings of Integers of Lextension’, see F.17). He went on to posts at Oxford, Queen Mary College London, and Cambridge, before being appointed Professor of Pure Mathematics at UMIST. ‘Galois (Ph.D. E.91 E.92 E.93, E.94 Curriculum vitae ca 1997 Correspondence re workin progress, including preparation of papers, newsof colleagues 1977-1979 Correspondence re joint paper ‘The arithmetic theory of local Galois Gauss sums for tame characters’, Phil. Trans. R. Soc. Lond. A298 (1980) (see C.72), Taylor's proof of Frohlich’s conjecture U=t(w), newsof colleagues, etc. 1980 2 folders. E.95 Correspondence and papers 1984, 1986, n.d. Includes photocopied manuscript ‘Comments on “Local root numbers etc” ’ by Frdhlich, annotated ‘Martin’ and manuscript working beginning ‘For simplicity take G of order Iq (The method extends to Iq without difficulty)’ annotated ‘File under Taylor’. A. Frohlich NCUACS 153/3/07 E.96, E.97 E.98 Correspondence, E.1-E.125 preprints Typescript information: characteristics’, Arakelov Euler characteristics’ ‘E-constants ‘Epsilon by and constants Martin sent to Frohlich for Euler equivariant Arakelov and 2 folders. E.99-E.104 Ullom, S.V. After a period at the Princeton, New Jersey, UniversityofIllinois at Urbana-Champaign. Institute USA, for Advanced Study, Ullom moved to the 65 2000 1974-1992 1967-1988 E.99 E.100 E.101 E.102 For joint correspondence with |. Reiner see E.63. Correspondence re work in progress on classgroups, and Ullom’s lectures at King’s College London, spring 1969. 1967-1971 and_ papers,’ Correspondence Ullom’s demonstration of ‘theorem for G a p-group, not necessarily abelian, of order p 1 n 2 0’, and correspondence re Reiner, Ullom and Frohlich, ‘Class groups and Picard groups of orders’, Proc. Lond. Math. Soc. 3rd ser. vol. 29 (1974) (see C.55), and other work in progress including Correspondence and papers, grant application (unsuccessful) to spend sabbatical year 1976- 1977 at King’s College including Ullom’s 1972-1974 1975-1976 Ullom did come to London, supported by the University of Illinois. Correspondence arising from Ullom’s sabbatical, work in progress on Bernoulli numbers and tame extensions, news of colleagues, visit to London 1979, etc. 1977-1979 E.103 Correspondencere work in progress including Gauss sums 1980-1981 A. Frohlich NCUACS 153/3/07 66 Correspondence, E.1-E.125 Correspondence, including work of Ullom’s student S.B. Watt (See F.23), work on Galois module structure 1982-1988 E.104 E.105 1980-1988 1968-2000, n.d. E.106-E.111 Wall, C.T.C. Wall was Professor of Pure Mathematics at the University of Liverpool. He co-authored a number of papers with Frohlich. correspondence The workings by both parties. includes many mathematical E.106 Correspondence, chiefly re Brauer groups, and exchange of drafts and offprints 1968 Wall and Frohlich collaborated on a paper ‘Equivariant Brauer groupsin algebraic number theory’, Bull. Soc. math. Fr. vol. 25 (1971) (see C.44). E.107 Correspondence, chiefly re Brauer groups and [-graded category, and joint paper delivered on equivariant K-theory, delivered at conference in Hull, published as ‘Foundations of equivariant algebraic K-theory’. In Proceedings of Hull Conference (ed. R.M.F. Moss and C.B. Thomas). Berlin: Springer, 1969. (See C.40) Includes ‘Construction of some basic categories’ by Wall, 8pp manuscript. 1969 E.108 Correspondence, including progress on joint paper on Brauer groups 1970-1971 ‘Equivariant in Wall and Frohlich continued their work on Brauer groups, co-authoring algebraic number theory’, Bull. Soc. math. Fr. vol. 25 (1971), see C.44. They also appear to have been preparing another major paper on the subject (see C.45, C.45A, C.102, C.103). This was never published. Brauer groups A joint paper ‘Equivariant Brauer groups’ was published in Contemp. Math. vol. 272 (2000), see C.110. A. Fréhlich NCUACS 153/3/07 67 Correspondence, E.1-E.125 E.109 E.110 Correspondenceincluding work in progress on joint paper with Wall, ‘Graded monoidal categories’, Compos. Math. vol. 28 (1974) (see C.53) 1972-1973 In his letter of 8 December 1972 Frohlich had written, ‘I feel rather downhearted about the paper after your last letter and | wonderif it will ever be completed’. Correspondence and papersre work in progress, including classgroups of 2-cyclotomic fields and Swan modules (r) for 1 quaternion of order 2” 1974 Also includes typescript draft of ‘Norms of units in group rings (Corrigendum)’ by Wall. E.111 Correspondence, including work on equivariant Brauer groups 1976-1983, 2000, n.d. Also includes undatedletters. E.112 Walter, C.D. 1975-1979 Walter was based at Cambridge before taking up a post at University College Dublin, Frohlich was an examiner of Walter’s Ph.D. thesis. Ireland. E.113 Wehrfritz, B.A.F. 1972-1981 Wehrfritz was based at Queen Mary College London. Correspondencere problems in field theory. E.114 Weiss, A 1991 Weiss was based at the University of Alberta, Edmonton, Canada. Correspondencere Galois stable lattices. E.115, £.116 Wicke, G. 1967-1976, n.d. Wicke held a tutorial studentship in the King’s College A. Frohlich NCUACS153/3/07 68 Correspondence, E.1-E.125 Department Mathematics to Germany he took up a postat the Free University of Berlin. Frohlich was external examiner for his Ph.D. thesis in 1975. 1962-1963. return On E.115 E.116 Correspondence, chiefly re career 1967-1976 Photocopied Resolventen’, annotated ‘File under Wicke’ manuscript draft ‘Uber allgemeine N.d. E.117 Wielandt, H. 1959 Includes correspondencere Frohlich’s work on near-rings. E.118-E.121 Wilson, S.M.J. 1973-ca 1994 Wilson was a postgraduate student of Frohlich’s at King’s College in the late 1960s-early 1970s (Ph.D. ‘On the K- theory of Twisted Group Rings’ awarded 1972). He was appointed Research Assistant at King’s in 1971 and Temporary Lecturer in 1972, before appointment in 1973 as Lecturer in Pure Mathematics at the University of Durham. E.118 Curriculum vitae E.119 E.120 E.121 ca 1994 1973-1976 Correspondence, including re joint paper with M. Keating, ‘The classgroup of Quaternion and Dihedral 2-groups’, Mathematika vol. 21 (1974) (see C.51), and photocopied manuscript working ‘Kernel groups of twisted group rings over rings of global integers and of orders associated with monomial representations’ Correspondencere work in progressand visits 1977-1978 Correspondencere workin progress 1979-1990 Includes typescript draft ‘Unsuccessful generalizations of tame results to the wild case’, annotated ‘Wilson’. Correspondence,E.1-E.125 A. Frohlich NCUACS 153/3/07 E.122 W. E.123 Y.,Z. E.124 Zelinsky, D. Zelinksy was based at Northwestern University, Evanston, Illinois. E.125 First name and unidentified 69 1971-1988 1965-1984 1968, 1975 1972-1991, n.d. A. Frohlich NCUACS 153/3/07 SECTION F THESES AND EXAMINATIONS, F.1-F.33 F.1-F.29 THESES 70 1961-1990, n.d. 1961-1989 Theses of Ph.D. students supervised or examined by Frohlich. F.1-F.20 King’s College London 1961-1982 F.1 F.2 F.3 F4 F.5 F.6 F.7 F.8 ‘Near-rings with descending chain conditions’ by Ronald Robert Laxton, April 1961 1961 ‘Galois Groups September 1961 of Polynomials’ by Raimundo Chela, 1961 ‘Topological September 1964 Near Rings’ by Veluppillai Tharmaratnam, 1964 ‘Some invariants of algebras’ by Abraham Lue, November 1964 ‘Sometopics in the theory of categories’ by Syed Afzal-ul Huq, November 1964 ‘Module Theory over Generalized Ore Rings’ by Mohammed Abdur Rauf Qureshi, September 1965 ‘Some topics in the Theory of Orders’ by Michael Edward Keating, 1967 ‘Hermitian Forms over Algebras’ by Allan William McEvett, 1967 1964 1964 1965 1967 1967 A. Fréhlich NCUACS 153/3/07 F.9 F.10 F.11 F.12 F.13 F.14 F.15 F.16 F.17 F.18 F.19 Theses and examinations, F.1-F.33 ‘Irreducibility criteria and some topics in Galois theory’ by Howard Kleiman, 1968 ‘Ideals over Orders in Commutative Separable Algebras’ by Martin Singer, 1970 ‘Ramification theory in the category of commutative rings with operators’ by A.D. Barnard, October 1971 71 1968 1970 1971 ‘Representations Bushnell, February 1972 of 23-Graded Groups’ by Colin John 1972 ‘On the K-theory of Twisted Group Rings’ by Stephen Mark Johnson Wilson, March 1972 ‘Varieties of O-groups and associated functors’ by Joao Candido de Antas Furtado Coelho, November 1972 1972 1972 ‘The Brauer Group of Dimodule Algebras’ by F.W. Long, 1972 1972 ‘Picard and Hermitian Picard Groups of Non-Commutative Orders’ by Michael William Rutter, 1975 ‘Galois Module Structure of the Rings of Integers of /- extension’ by Martin John Taylor, 1976 ‘Monomial Representations and Galois Module Structure’ by Adrian Maurice Nelson, May 1979 ‘Realizable Classes in the Class Groups of Integral Group Rings’ by Celia Ann Glass, July 1979 1975 1976 1979 1979 A. Frohlich NCUACS 153/3/07 72 Theses and examinations, F.1-F.33 F.20 ‘Class Groups of Group Rings over Quadratic NumberFields’ by Soroosh Homayouni 1982 1982 F.21, F.22 University of Cambridge 1976, 1989 F.21 F.22 ‘Class numberrelations in algebraic numberfields’ by Colin Donald Walter, April 1976 ‘Factorisability, Group Lattices and Galois Module Structure’ by David Burns, December 1989 F.23 University ofIllinois ‘Genus Fields and central extensions of number fields’ by Stephen Bruce Watt, 1983. 1976 1989 1983 F.24-F.28 University of Bordeaux| 1975-1986 F.24 F.25 F.26 F.27 ‘Proprietes galoisiennes des anneaux d’entiers [...]’ by Jean Cougnard, March 1975 ‘Structure galoisienne des anneaux d’entiers’ by Philippe Cassou-Nogués, October 1977 ‘Anneaux d’entiers et ordres associés’ by Anne-Marie Bergé, April 1979 ‘K-théorie algébrique et structure galoisienne des anneaux d’entiers’ by Jacques Queyrut, March 1980 1975 1977 1979 1980 A. Frohlich NCUACS153/3/07 73 Theses and examinations, F.1-F.33 F.28° ‘Sur la construction a noyau d’ordre p des p-extensions galoisiennes’ by Richard Massy, March 1986 1986 F.29 Research Students Two lists of Fréhlich’s research students, one from online ‘Mathematics Genealogy Project’ http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=46030 (printed out May 2007). F.30-F.33 EXAMINATIONS Examination calculations of answers. and test papers, some with Frdhlich’s F.30 F.31 F.32 F.33 Cambridge Mathematical Tripos Cambridge Mathematical Tripos Cambridge Mathematical Tripos Other tests and examinations 1982-1990, n.d. 1980 1981 1982 1982-1990, n.d. 74 A. Frohlich NCUACS 153/3/07 INDEX OF CORRESPONDENTS ADAMS, John Frank ALEXANDER VON HUMBOLDT FOUNDATION AMERICAN MATHEMATICAL SOCIETY ARMITAGE, J.V. BAK, Anthony BAMBAH, R. Prakar BANIEQBAL, B. BARTELS, H.-J. BAYER, Eva BERGE, Anne-Marie BERNSTEIN, Leon BOLTJE, Dr BONDI, Sir Hermann BRINKHUIS, Jan BROWN, LawrenceG. BURNS, David BUSHNELL, Colin John BYOTT, N.P. CALIFORNIA INSTITUTE OF TECHNOLOGY CALLAHAN, T. CARLETON UNIVERSITY CASSELS, John William Scott (‘lan’) CASSOU-NOGUES, Philippe, CHAPMAN, Robin J. E.1 A.33 D.9 E.72 E.15 E.15 E.15 E.15 E.2 E.3 See also F.26 E.15 E.15 A.23 D.15, E.4-E.7 E.68 B.56, B.57, E.8 See also F.22 E.9-E.14 See also F.12 E.15 D.2 E.36 A.36 E.16 See also C.36 See NOGUES E.20 A. Frohlich NCUACS 153/3/07 CHASE, Stephen U. CHINBURG, Ted C. COUGNARD, Jean Index of correspondents COXETER, Harold Scott Macdonald CUNNINGHAM, Jr, Frederic DEDECKER, Paul DING Qing-Ping DYER, Sir (Henry) Peter (Francis) SWINNERTON- EPSTEIN, David EREZ, Boas FEIT, Walter FRESNEL, Jean FRIEDMAN, Eduardo E.17A B.56, B.57, E.18 A.8, E.19 See also F.24 E.36 E.20 E.21 E.21 E.80 E.21 E.22 E.23 E.23 E.23 FROHLICH (née BROOKS), (Evelyn) Ruth A.8, A.9, A.11, A.13, A.14 FROHLICH, Sorrel Ruth Tamar FURUTA, Yoshiomi GALOVICH, Steven P. GARBANATI, Dennis GEYER, W.-D. GOLD, R. (‘Bob’) GOLDHABER, Jack GOLDMAN, O. GORMAN, Howard E. GRAS, Georges GREEN, James Alexander (‘Sandy’) A.11 E.23 E.24 E.25 D.8, E.26 E.29 E.29 E.29 E.29 E.27 E.28 A. Frohlich NCUACS 153/3/07 76 Index of correspondents GRUENBERG, Karl W. HALBERSTAM, H. HALL, Philip HASSE, Helmut HASSE, Henry Ronald HAYMAN, Walter Kurt HEILBRONN, Hans Arnold HENNIART, Guy HIGGINS, Philip HOLLAND, David HOOLEY, Christopher HSIA, John S HUQ, Syed Afzal-ul IWASAMA,Kenkichi JARDEN, Moshe JEHNE, Wolfram KAHN, Bruno KANI, Ernst KAPLANSKY,Irving KAWAMOTO, Fuminori KETTERER, Brian KLEIMAN, Howard KNESER, Martin KNUS, Max Albert E.29 E.39 E.30 E.31 See also E.26 A.19 E.39 A.24, E.32-E.36 See also C.63 D.10 E.39 E.37 E.39 E.38 E.39 See also F.5 E.39 E.39 D.34, E.39 E.46 E.40 D.23, E.46 E.41 E.46 E.46 See also F.9 E.42 E.43 A. Frohlich NCUACS 153/3/07 KOCH, Franz HALTER- KOCH, Helmut KURODA,Sige-Nobu KUYK, W. LANGLANDS, Robert LECOUTURIER, P. LEDERMANN, Walter LEHMER, Emma LEOPOLDT,Heinrich W LEVERHULME TRUST LEWIS, Don J. L! Delang LINFOOT, Edward Hubert Index of correspondents E.46 E.44 E.45 E.46 E.48 E.47 E.48 E.48 E.48 A.30 E.40 E.48 A.19 LONDON MATHEMATICAL SOCIETY A.11, A.14, A.28, A.34, D.29, D.31 LUBIN, Jonathan D. LUTHAR, Indar Singh McCULLOH, Leon R. MACDONALD, lan G. McEVETT, Allan William MARTINET, Jacques MILNOR, John NARKIEWICZ, Wladyslaw NELSON, Adrian Maurice NEUMANN, Peter M. NOGUES, Philippe, CASSOU- E.48 E.48 A.11, E.49 E.50 E.51 See also F.8 D.12, E.52-E.54 E.55 E.56 E.57 See also F.18 E.51 A.11, E.17 See also F.25 A. Frohlich NCUACS 153/3/07 78 Index of correspondents ODONI, Robert W.K. OJANGUREN, M. OPOLKA,Hans ORDE, H.L.S. OXFORD UNIVERSITY PRESS PATTERSON, S.J. (‘Paddy’) PERLIS, Robert POITOU, Georges QUEYRUT,J. RADO, Richard RAJWADE, A.R. REDEI, L. REICHARDT, Hans REINER, Irving REMMERT, R. RIEHM, Carl RITTER, Jurgen ROCQUETTE, Peter ROGERS, C. Ambrose ROSENBERG, Alex ROTH, Klaus F. ROYAL SOCIETY SCHARLAU, Winfrid SCHERTZ,Reinhard SEMPLE, JackG. D.18, E.59 E.58 E.59 E.59 E.59 E.61 E.60 E.61 E.61 See also F.27 E.36 E.69 E.62 E.69 E.63, E.64 C.77 D.9, E.69 C.101, D.32, E.65, E.66 E.67 E.36 E.55, E.68 A.31 A.8, A.24, A.25, A.33, D.5 E.80 E.70 E.80 A. Frohlich NCUACS 153/3/07 79 Index of correspondents SERRE, Jean-Pierre SILVERMAN, Joe SMITH, R.A. SNAITH, Victor SNEDDON, Ian Naismith STROOKER, Jan R. STUART, J. Trevor SWINNERTON-DYER, Sir Peter TATE, John T. TAUSSKY-TODD, Olga TAYLOR, Martin John THARMARATNAM, Veluppillai THE TIMES THOMAS, Charles Benedict THOMPSON, John G. THOMPSON, Richard B. TODD, John TODD, Olga TAUSSKY- E.71-E.77 E.80 E.80 D.33, E.78 A.22 E.79 A.14, E.80 See DYER E.81 E.82-E.90 D.26, E.91-E.97 See also F.17 E.98 See also F.3 A.37 A.13 E.98 E.98 E.83 See TAUSSKY-TODD ULLOM, Stephen V. E.63, E.99-E.104 UNIVERSITY COLLEGE OF NORTH STAFFORDSHIRE A.22 UNIVERSITY OF BRISTOL A.19, A.35 UNIVERSITYOF ILLINOIS AT URBANA-CHAMPAIGN UNIVERSITY OF IOWA UNIVERSITY OF LEICESTER D.7 D.30 A.21 A. Frohlich NCUACS 153/3/07 80 Index of correspondents UNIVERSITY OF LONDON IMPERIAL COLLEGE KING’S COLLEGE VAL, Patrick du VAUGHAN, R.C. VELEZ,William WALDSCHMIDT,Michel WALL, Charles Terence Clegg (‘Terry’) WALTER, Colin Donald WASHINGTON, L.C. WATERHOUSE, William C. WATSON, G.L. WATT, Stephen Bruce WEHRFRITZ, Bert A.F. WEISS, Al. WHARPLES, George WICKE, Gunter WIELANDT, Helmut WILES, Andrew WILSON, Stephen Mark Johnson WRIGHT, David J. YAHYA, Saiyed Mohammed ZEEMAN, Sir (Erik) Christopher ZELINSKY, Daniel A.32 A.23 E.36 E.105 E.105 E.122 E.106-E.111 E.112 See also F.21 E.122 E.122 E.122 E.122 See also E.104, F.23 E.113 E.114 E.122 E.115, £.116 E.117 E.122 E.118-E.121 See also F.13 E.122 E.123 E.123 E.124 A. Frohlich NCUACS 153/3/07 81 Index of correspondents ZINK, W.-W. E.123