FROHLICH_ALBRECHT
Catalogue of the papers and correspondenceof
Albrecht Frohlich FRS
(1916-2001)
NCUACScatalogue no. 153/3/07
by Timothy E. Powell and Peter Harper
A. Fréhlich
NCUACS 153/3/07
Title:
Compiled by:
Timothy E. Powell and Peter Harper
Description level:
Fonds
Depositedin:
Date of material:
1948-2006
Extent of material:
21 boxes, ca 460 items
Catalogue of the papers and correspondenceof Albrecht
Frohlich (1916-2001), mathematician
NCUACS catalogue no. 153/3/07
© 2007 National Cataloguing Unit for the Archives of Contemporary Scientists,
University of Bath.
College Archives, King’s College London
Reference code:
GB 0100 KCLCA K/PP156
A. Frohlich
NCUACS 153/3/07
The work of the National Cataloguing Unit for the
Archives of Contemporary Scientists in
the production of this catalogue is made possible
by the support of the
(
aS
yi,
Arts & Humanities
Research Council
A. Frohlich
NCUACS 153/3/07
NOT ALL THE MATERIAL IN 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
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LIST OF CONTENTS
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
ee
SECTION F
THESES AND EXAMINATIONS
F.1-F.33
INDEX OF CORRESPONDENTS
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GENERAL INTRODUCTION
PROVENANCE
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 youngestof 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 Fréhlich went to the Wittelsbacher
Gymnasium butwith the rise to powerof the Nazis Frohlich and his parents left Germany for France
in 1933, and the following year movedto Palestine to join Betti (Herbert had gone to the University of
Leningrad in 1934, then to the University of Bristol in 1935).
In Palestine Frdhlich worked as a
plumber and then as an electrician in a railway workshop.
under H.A. Heilbronn. Frohlich completed his doctoral thesis in October 1950 (Ph.D. awarded 1951).
his visits abroad and bringing up their children.
Frohlich was Assistant Lecturer in Mathematics at the University of Leicester 1950-1952 and Lecturer
1945 Herbert, now Reader in Physics at the University of Bristol, arranged for his younger brother to
While an undergraduate at Bristol Frohlich met a medical student, Ruth Brooks, whom he married in
in Pure Mathematics at the University College of North Staffordshire 1952-1955.
In 1955 he was
December 1945. He graduated with First Class Honours in 1948 and began post-graduate research
join him at Bristol.
Fréhlich was accepted as a student and began his studies in mathematics in
Frohlich had endedhis formal education at the age of seventeen when he fled Germany. However,in
1950. She becamea doctorin general practice, while also accompanying her husband on manyof
1984). He also made many conferencevisits to the USA, Germanyand France.
appointed Reader in Mathematics at King’s College London. Subsequently he became Professor of
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
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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, which still 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 knownasarithmetic 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 development of algebraic number theory in many ways; he has
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
Bordeaux (1986) and Bristol (1998) and the Alexander von Humboldt Foundation Humboldt Research
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
Society’s Senior Berwick Prize in 1976. Fréhlich received honorary doctorates from the universities of
(2005), 149-168. A copyis atA.6.
Award for the Scientific Cooperation between Great Britain and Germany in 1992. He waselected a
For a full account of Frdhlich’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
Fellow of the Royal Society in 1976. He died 8 November 2001.
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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 Frdhlich’s
life, held in the Chapel of Robinson College Cambridge, 10 February 2002, and othertributes. 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 papersrelating 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 Fréhlich’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.
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),
his first article ‘The representation of a finite group as a group of automorphisms on finite Abelian
group’, Quarterly Journal of Mathematics 2nd ser. vol. 1 (1950), to ‘Equivariant Brauer groups’ (with
1994.
References are made to the Bibliography at A.16 in the form Bibliog. no. ....
The material
accompanying mathematical workings. The section also includes a few unpublished drafts, including
mainly takes the form of offprints, but there are also some drafts of papers and occasionally
Section C, Publications, presents comprehensive documentation of Frdhlich’s published output, from
work with C.T.C. Wall on Brauer groups, ‘Galois modules and the functional equation’, and a possible
programmes, and texts or abstracts of lectures delivered are few.
Section D, Visits, conferences and lectures, provides patchy coverage of Fréhlich’s conference
attendance and overseas visits 1956-1998 but includes documentation of his participation in
Germany and some Visiting Professorships.
The material in the main comprises invitations and
draft of a book on ‘mathematical theory of ostensive and consequently of empirical predicates’.
influential mathematics meetings held at the Mathematisches Forschungsinstitut, Oberwolfach,
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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 Fréhlich’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 Frohlich’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
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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
OBITUARIES AND MEMOIRS
2001-2006
obituary
for
University
Frohlich died on 8 November 2001.
24
December 2001,
by
V.
of
Bristol
Obituaries from The Times, 30 November 2001; and
Independent,
Armitage
(including typescript drafts, and print-out of online version)
Obituary for the Heidelberg Academy of 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
Fellows of the Royal Society vol 51 (2005), 149-168
‘Albrecht Frohlich (22 May 1916 - 8 November 2001)’ by
B.J.
Biographical Memoirs of
Birch and MJ. Taylor,
Online obituary by J.J. O'Connor and E.F. Robertson from
MacTutor History of Mathematics
(http:/www-history.mcs.st-andrews.ac.uk/Biographies/Frohlich.html)
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Biographical, A.1-A.37
Typescript drafts
2 folders.
Offprint
‘Albrecht Frohlich 1916-2001’ by M.J. Taylor, Bulletin of the
London Mathematical Society vol 38 (2006), 329-350
Offprint
MEMORIAL SERVICE AND OTHER TRIBUTES
2001-2006
Frohlich family letter of thanks for condolences received on
Albrecht Fréhlich’s death
With twoletters of condolence.
of the
life
of Ali
Fréhlich’, The Chapel,
Draft and printed Order of Service
Tributes to Frohlich from colleagues
L. McCulloh, P. Cassou-Nogués, J.
C.B. Thomas.
‘Celebration
Robinson College Cambridge, 10 February 2002
Arithmetic and Geometry,
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
Orders
in
Ritter, V. Armitage,
Correspondence arising
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Biographical, A.1-A.37
dedicated to the memory of Fréhlich, London Mathematical
Society newsletter, April 2002
and
equivariant
Arakelov-Euler
‘e-constants
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 Fréhlich from C.B. Thomas, 2005, referring
to dedication of his book Representations of Finite and Lie
Groupsto Albrecht Frohlich.
Fréhlich Prize
2002, 2006
This prize, to be awarded by the London Mathematical
Society for ‘new, original and extremely innovative workin
Mathematics’ was established by Ruth Frdéhlich 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
1960s-2002
Curricula vitae
1960s, 1990s
bibliography has been used in
referencing
the
AUTOBIOGRAPHICAL
This
publications in section C.
Entry for Frohlich for International Who’s Who 2002
Copyof Fréhlich’s entry for Personal Records of Fellows of
the Royal Society; copy of citation of election (1976)
Manuscriptlist of books by Frohlich.
Bibliography
1976, 1987
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Biographical, A.1-A.37
A.19-A.35
CAREER, HONOURS AND AWARDS
1948-2005
Student, University of Bristol
1948-1950
Fréhlich came to Bristol at the end of the Second World
War at the suggestion of his brother Herbert who was
Readerin Physics at the University.
studies
Although Fréhlich had ended his formal education at the
age of seventeen he was accepted as a student and began
his
in mathematics in December 1945. He
graduated in 1948 and began doctoral research under H.A.
Heilbronn.
Fréhlich completed his Ph.D. thesis in October
1950 (awarded 1951).
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
1950-1951
1951-1952
Correspondencere appointment.
Correspondence re appointment.
Assistant Lecturer in Mathematics, University of Leicester
‘On some topics in the theory of representation of groups
and in classfield theory’, Ph.D. thesis, October 1950
Lecturer in Pure Mathematics, University College of North
Staffordshire, Keele
1954-1981
Reader
of
Mathematics (1962), Head of Department (1969), Emeritus
Professor (1981).
Appointments at King’s College London
Correspondencere appointments.
in
Pure
Mathematics
(1955),
Professor
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Biographical, A.1-A.37
A.24-A.27
Election to the Fellowship of the Royal Society, 1976
1964-1977
as_
such
“effective
Frohlich’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
number-fields and the
module-structure
discovery
part
conjectural) with the behaviour of the associated zeta- and
L-functions has attracted widespread interest. See also
A.17.
of a totally unsuspected
procedures’,
algebraic
relation
(in
of
Correspondence re proposal
1964, 1968
Notification in press; list of Fellows elected 1976
Letters of congratulation
1976-1977
In chronological order.
Not indexed.
2 folders.
Notice from King’s College London.
Correspondencere arrangements for presentation.
Election to Fellowship, Robinson College Cambridge
London Mathematical Society Senior Berwick Prize for
1976
Report to the Leverhulme Trust 1987.
Frohlich was awarded a Fellowship to support his ongoing
research into Galois Gauss sums.
Includes draft of application for Fellowship 1984, and
Leverhulme Emeritus Fellowship
1984-1989
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Biographical, A.1-A.37
Honorary Doctorate, University of Bordeaux, March 1986
Notice, letter of congratulation.
Senior Research Fellow, Imperial: College
1988-1996
Correspondence re appointment.
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.
London Mathematical Society de Morgan Medal for 1992
1992, 1993
to
1998, 2005
Honorary Doctorate, University of Bristol
received the medal ‘for
his many important
Frohlich
contributions
most
important achievement is the creation of that body of
knowledge now knownas arithmetic Galois module theory’.
algebraic number theory...his
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).
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).
1975
Photocopy
blackboard; correspondence from
Ottawa, Canada re use of photograph of Frohlich, 1974
lecturing
at
University,
N.d.,1974,
1975, 1981
of
photograph
of
Frdhlich
A.36, A.37
MISCELLANEOUS
Carleton
N.d.,1974-
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Biographical, A.1-A.37
‘University cuts’, Letter published in The Times, 26 March
1981
Typescript letter as sent; publishedletter.
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SECTION B
RESEARCH, B.1-B.101
?1950s-
1996, n.d.
presented
This section is chiefly manuscript mathematical workings,
notes and drafts
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 number of short paginated
sequences, and some may have been written as early
drafts for publication. Few are dated.
possible
far as
as
Fréhlich’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.
‘Absolute conductor & resolvent theory’
Contents of folder so inscribed.
‘On algebraic closure’
ca 1965
‘Archimedean theory etc’ and ‘Norms’
‘Archimedean theory. Duality in real vector spaces’
Bundle of folders so labelled. Some of the folders were
themselves inscribed and the contents in some cases
further subdivided.
10pp typescript.
‘Normsof operators’ and ‘Characters with transformations’
‘Some remarks on Artin conductors’
‘Geometry of numbers’
‘Norms’
3 folders.
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Research, B.1-B.101
‘Relative Brauer + Picard groups‘ and ‘Various results for
change ofrings’
1969, n.d.
Contents of folder so inscribed.
1969.
Some workings dated
2 folders.
‘A canonical class for Galois extensions of number fields’
Manuscript and typescript workings so titled; typescript
pages and manuscript and photocopied manuscript notes
found therewith.
‘Canonical factorisation and Martinet’s conjecture’
Photocopy manuscript workings sotitled, 9pp and 14pp.
‘Notes for further work on conductors’
Contents of folder so inscribed.
B.15-B.31
Decomposition
?1950s
‘Decomp. 1 draft. A Frohlich’
Bundle of folders inscribed ‘Dec’, ‘Decomp’ and similar:
work on the decomposition of primes.
This was work begun by Frdéhlich in the 1950s and some of
the material appears to have been drafted with publication
in mind.
‘Dec. Chp 4’
‘Drafts, decomp.’
‘Dec. Chpt. 3’
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Research, B.1-B.101
B.19-B.22
‘Final draft. Prime decomposition [...]’
4 folders.
‘Decomposition. Numerical examples’
‘Dec. (a) p-adic problem. (b) local fields for p+2’
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.
3 folders.
B.28-B.30
‘Notes for dec. paper’
‘Dec. Local fields over R2’
With later manuscript note ‘Extensions of R»2 of certain
[?unipotency] classes: explicit calculations’.
typescript ‘printout’; manuscript workings.
‘On the density of discriminants of cubicfields II’
‘§ 2 The class of a principal factorisation’
Typescript note with manuscript annotation.
Photocopied
manuscript
and
typescript
draft;
4pp
N.d, 1996
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Research, B.1-B.101
B.34, B.35
‘First write-up concerning factorisibility’
2 folders.
B.36-B.38
‘Fields over P,’
folder
(retained
at B.38) bears mathematical
Original
working.
3 folders.
Manuscript and photocopied manuscript workings, first
page beginning ‘Notions of filtered ring [...]’
‘1 Finite fields’
Photocopied manuscript working.
e
e
Galois Gauss sums — resolvents
Galois stabil lattices’
First page is inscribed ‘Olga’.
‘Gal. Gauss Notes’
Includes ‘Examples (I alwaysfinite), 20pp.
Manuscript working, first page beginning ‘T a finite group,
Br its Burnside ring [...]’
Manuscript and photocopied manuscript workings, with
later covering note
‘handwritten part of papers
‘On wild Galois extensions of number fields’
6pp typescript progress report on work on a Galois
extension N/K of number fields;
manuscript working
beginning ‘Here N/Kis a Galois extension offields’.
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Research, B.1-B.101
‘Reformulation of some results on Galois module structure’
Manuscript
and
circulation only)’.
typescript
drafts
marked
‘(Informal
‘§ 2 Introduction to Gauss sums’
39pp manuscript working.
‘Gauss sums’
ca 1983
Typescript draft, ‘This is a report on some aspects ofjoint
work with C.J. Bushnell’ (may relate to Gauss sums and p-
adic division algebras, at C.78).
‘A programmeforelliptic Gauss sums’
This may have been intended for delivery as a lecture.
‘Wild Gauss sums’
B.51, B52
‘Genus Classfreq.’
B.53-B.55
‘Graded categories’
Contents of folder so inscribed divided into two for ease of
reference.
Contents of envelope so inscribed divided into three for
ease of reference.
by Frohlich.
Includes correspondence with T.C. Chinburg and D. Burns
re work on the Gras conjecture, with manuscript workings
Contents of folder so inscribed divided into three for ease
of reference.
B.56-B.58
‘Gras conjecture’
1989, 1990
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Research, B.1-B.101
Untitled manuscript working beginning ‘The idele group of
a numberfield E’
‘Integral or Radical modules. II°. Functions based on
Resolvents’
Contents
internally according to the folder inscription.
inscribed,
folder
so
of
further
subdivided
‘|-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.
B.68-B.70
7pp typescript.
With later manuscript note.
‘[...] Categories of modules’
‘Some comments on the map t’
ca 1980
‘Normswrite up Jan 77’ and ‘Main write up’.
55pp typescript with list of contents
Contents of folder so inscribed.
‘“Monomial” Conductor’
2 folders.
1p only.
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Research, B.1-B.101
B.69, B.70
Manuscript workings
2 folders.
‘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.
‘p-adic theory’
Contents
internally by label.
of
folder
so
inscribed,
further
subdivided
‘A quadratic-elliptic Stickelberger element’
11pp photocopied manuscript working not in Frdhlich’s
hand.
‘The quadratic reciprocity law’
‘The category of rings with operators’
5pp typescript, with later manuscript note ‘an interesting
(and strange) argument proving the quadratic reciprocity
law)’.
Bundle of workings so labelled.
‘Calculations with resolvents and cocycles
root numbers’
‘Resolvents’
Contents of folder so labelled.
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Research, B.1-B.101
‘Siegel functions’
‘Siegel modular forms and a candidate for a v,4-periodic
cohomology theory’
5pp photocopied manuscript working not in
hand.
Frdhlich’s
‘Proof of the strong approximation theorem by additive
duality’
2pp photocopied typescript.
‘Trace forms and related matters’
Photocopied
manuscript
circulation June 26, 1990’.
draft
marked
‘Restricted
‘The twisting factor’
Untitled workings, dated 22 and 23 January 1969
‘Weak equivalence for tame representations of the Weil-
group QO of a local field F’
of reference: mathematical workings.
Untitled working, dated 26 April 1980, with ‘Supplement to
my M.S. of 26 April’
Contents of folder so inscribed divided into three for ease
B.88-B.90
‘Old’
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SECTION C
PUBLICATIONS, C.1-C.125
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
ostensive
theory
on
of
‘The representation of a finite group as a group of
automorphismsona finite Abelian group’, Q. J. Math. 2nd
ser. vol. 1 (1950) 270-283. Bibliog. no. 1
Offprint.
‘On the class group ofrelatively Abelian fields’, Q. J. Math.
2nd ser. vol. 3 (1952), 98-106. Bibliog. no. 2
Photocopied offprint.
Offprint.
Offprint.
‘On the absolute class group of Abelian fields’, J. Lond.
Math. Soc. vol. 29 (1954), 211-217. Bibliog. no. 4
‘On fields of class two’, Proc. Lond. Math. Soc. 3rd ser. vol.
4 (1954), 235-256. Bibliog. no. 3
‘The generalization of a theorem of L. Rédei’s’, Q. J. Math
2nd ser. vol. 5 (1954), 130-140. Bibliog. no. 6
‘A note on the class field tower’, Q. UJ. Math. 2nd ser. vol. 5
(1954), 141-144. Bibliog. no. 5
Offprint.
Offprint.
A. Frohlich
NCUACS 153/3/07
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 (Il)’. 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.
pp.
2,
Int.
20-21.
Offprint (of abstract).
J.C.
Shepherdson)
(With
of
polynomials in a finite number of steps’, Math. Zeitschr. vol.
62 (1955), 331-334. Bibliog. no. 10
factorisation
‘On
the
Soc.
Il.
Math.
Offprint.
Offprint.
3rd ser.
(With J.C. Shepherdson) ‘Effective procedures in
field
theory’, Phil. Trans. R. Soc. Lond. vol. A248 (1956), 407-
432. Bibliog. no. 11
‘Distributively generated near-rings. |. Ideal theory’. Proc.
vol. 8 (1958), 76-94 and
Lond.
‘Distributively generated
Representation
theory’. Proc. Lond. Math. Soc. 3rd ser. vol. 8 (1958), 95—
108. Bibliog. nos. 12 and 13
Offprint.
‘The near ring generated by the inner automorphismsof a
finite simple group’, J. Lond. Math. Soc. vol. 33 (1958), 95—
107. Bibliog. no. 14
Photocopiedoffprints.
near-rings.
A. Frohlich
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
‘Some more general nonsense’
‘§ More abstract nonsense’
Duplicated typescript paginated 99-115.
B.96-B.101
Miscellaneous mathematical workings
6 folders.
A. Frohlich
NCUACS 153/3/07
Publications, C.1-C.125
‘On a method for the determination of class factors in
number fields’, Mathematika vol. 4 (1957),
113-121.
Bibliog. no. 15
Offprint.
‘The restricted biquadratic residue symbol’, Proc. Lond.
Math. Soc. 3rd ser. vol. 9 (1959), 189-207. Bibliog. no. 16
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.
Offprints.
Offprints.
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
Il’,
Mathematika vol. 6 (1959), 142-146. Bibliog. nos. 18 and
19
finite number fields.
‘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
210; and ‘On groups over a d.g. near-ring (Il): Categories
‘The discriminants of relative extensions and the existence
of integral bases’, Mathematika vol. 7 (1960), 15-22.
Bibliog. no. 22
‘On groups over a d.g. near-ring (I): Sum constructs and
free R-groups’, Q. J. Math. 2nd ser. vol. 11 (1960), 193—
A. Frohlich
NCUACS 153/3/07
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
number fields’, Acta Sci. Math. Szeged vol. 21 (1960),
229-246. Bibliog. no. 25
Offprint.
‘Non Abelian Homological Algebra. |. Derived functors and
satellites’, Proc. Lond. Math. Soc. 3rd ser. vol. 11 (1961),
239-275; ‘Non Abelian Homological Algebra. ||. 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.
Offprints.
Offprint.
Offprint.
‘Discriminants and module invariants over a Dedekind
domain’, Mathematika vol. 8 (1961), 170-172. Bibliog. no.
31
‘On the /-class group of the field P('vm)’, J. Lond. Math.
Soc. vol. 37 (1961), 189-192; ‘A remark on the classfield
tower of the field P(’Vm)’, J. Lond. Math. Soc. vol. 37
(1961), 193-194. Bibliog. nos. 29 and 30
‘The module structure
over
Dedekind domains’, J. reine angew. Math. vol. 209 (1962),
39-53. Bibliog. no. 32
of Kummer extensions
(With J.-P. Serre & J. Tate) ‘A different with an odd class’,
J. reine angew. Math. vol. 209 (1962), 6-7. Bibliog. no. 33
A. Frohlich
NCUACS 153/3/07
Publications, C.1-C.125
Photocopiedoffprint.
‘On non ramified extensions with prescribed Galois group’,
Mathematika vol. 9 (1962), 133-134. Bibliog. no. 34
Offprint.
‘Baer invariants of algebras’, Trans. Am. Math. Soc. vol.
109 (1963), 221-244. Bibliog. no. 35
Offprint.
‘Galois algebras and their homomorphisms’, J.
angew.Math. vol. 216 (1964), 1-11. Bibliog. no. 36
reine
22pp manuscript draft, differently titled, headed ‘Original’;
offprint.
Offprint.
Offprint.
Offprint.
‘Some topics
Oberwolfach Ber. vol. 2 (1966), 59-83. Bibliog. no. 38
of module conductors’,
theory
the
in
for modules over commutative
This is an expanded version of Froéhlich’s Oberwolfach
lecture on module conductors.
‘Invariants
separable
orders’, Q. J. Math. 2nd ser vol. 16 (1965), 193-232.
Bibliog. no. 37
Offprint.
‘Resolvents, discriminants, and trace invariants’, J. Algebra
vol. 4 (1966), 173-198. Bibliog. no. 39
‘Radical modules over a Dedekind domain’, Nagoya Math.
J. vol. 27 (1966), 642-662. Bibliog. no. 40
A. Fréhlich
NCUACS153/3/07
Publications, C.1-C.125
‘Quadratic forms “a la” local theory’, Proc. Camb. Phil. Soc.
vol. 63 (1967), 579-586. Bibliog. no. 41
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
Offprint.
(With J.V. Armitage) ‘Class numbers and unit signatures’,
Mathematika vol. 14 (1967), 94-98. Bibliog. no. 43
Offprint.
‘Homology of categories with quotients and K-theory’, not
listed in Bibliog.
Photocopied typescript paginated I-V, 1-57, dated ‘June
1967’.
Formal groups, Lecture Notes in Mathematics no. 74,
Berlin: Springer, 1968. Bibliog. no. 46
(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’, J. Algebra vol. 12
(1969), 114-133. Bibliog. nos. 44 and 45
Bound copyas published by Springer
‘Lecture notes of a course given at
London’, 1966-1967.
King’s College,
Offprints.
?Pre-publication bound copy
A. Frohlich
NCUACS 153/3/07
Publications, C.1-C.125
(With C.T.C. Wall) ‘Foundations of equivariant algebraic K-
theory’. In Proceedings of Hull Conference (Lecture Notes
in Mathematics no.
108) (ed. R.M.F. Moss and C.B.
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
Offprint.
‘On the classgroup ofintegral grouprings of finite Abelian
groups’, Mathematika vol. 16 (1969), 143-152; and ‘On the
classgroup of integral group rings offinite Abelian groups.
Il, Mathematika vol. 19 (1972), 51-56.
Bibliog. nos. 49
and 54
1969, 1972
Offprints.
Offprint.
Offprint.
See also C.45, C.45A, C.102, C.103, E.106-E.108.
(With C.T.C. Wall) ‘Equivariant Brauer groups in algebraic
numbertheory’, Bull. Soc. math. Fr. vol. 25 (1971), 91-96.
Bibliog. no. 51
‘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
See also C.44, E.106-E.108.
C.45, C.45A
(With C.T.C. Wall) ‘Generalisations of the Brauer group |’.
Notlisted in Bibliog.
The second part of this may be the draft at C.102, C.103.
A. Frohlich
NCUACS 153/3/07
Publications, C.1-C.125
53pp duplicated typescript
Photocopied manuscript
‘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
integral
normal
Offprint.
Offprint.
Offprint.
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
‘The Picard group of noncommutative rings, in particular of
orders’, Trans. Am. Math. Soc. vol. 180 (1973), 1-45.
Bibliog. no. 56
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
‘Artin root numbers, conductors and representations for
generalised quaternion groups’, Proc. Lond. Math. Soc.
vol. 28 (1974), 402-438. Bibliog. no. 57
A. Frohlich
NCUACS 153/3/07
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
Offprint.
(With C.T.C. Wall) ‘Graded monoidal categories’, Compos.
Math. vol. 28 (1974), 229-285. Bibliog. no. 60
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.
Offprint.
J.
reine
Bibliog. no.
‘Locally free modules over arithmetic orders’,
angew. Math. vol. 274/275 (1975), 112-124.
63
(With I. Reiner and S.V. Ullom) ‘Class groups and Picard
groups of orders’, Proc. Lond. Math. Soc. 3rd ser. vol. 29
(1974), 405-434. Bibliog. no. 62
vol. 15 (1975), 353-363. Bibliog. no. 65
‘Galois module structure and Artin L-functions’, Soc. Math.
Fr. Astérisque vol. 24-25 (1975), 9-13. Bibliog. no. 64
Offprint.
Offprint.
‘Artin root numbers for quaternion characters’, Symp. Math.
A. Frohlich
NCUACS 153/3/07
Publications, C.1-C.125
Offprint.
‘Resolvents and trace form’, Math. Proc. Camb. Phil. Soc.
vol. 78 (1975), 185-210. Bibliog. no. 66
Offprint.
‘Module conductors and module resolvents’, Proc. Lond.
Math. Soc. 3rd ser. vol. 32 (1976), 279-321. Bibliog. no.
67
Offprint.
‘A normal integral basis theorem’, J. Algebra vol. 39
(1976), 131-137. Bibliog. no. 68
Offprint.
Offprint.
Offprint.
(With J.W.S. Cassels) ‘Hans Arnold Heilbronn 1908-1975’,
Biogr. Mem.Fell. R. Soc. vol. 22 (1976), 119-135. Bibliog.
no. 70
‘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.
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
tame
‘Arithmetic
extensions’, J. reine angew. Math. vol. 286/287 (1976),
380-440. Bibliog. no. 71
structure
module
Galois
for
A. Frohlich
NCUACS 153/3/07
Publications, C.1-C.125
group
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
In
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),
the
Promotion of Science, 1977. Bibliog. no. 76
Tokyo: Japan Society
25-42.
pp.
for
Math.
Offprint.
Offprint.
‘Non-Abelian Jacobi sums’. In Numbertheory and algebra
(ed.
H. Zassenhaus), pp. 71-75. New York: Academic
Press, 1977. Bibliog. no. 78
‘Rings of integers in tame extensions as Galois modules’,
Soc.
Fr. Astérisque vol. 41-42 (1977), 31-33.
Bibliog. no. 77
Théorie des Nombres,
‘Some problems of Galois module structure
wild
extensions’, Proc. Lond. Math. Soc. vol. 37 (1978), 193—
212. Bibliog. no. 79
Manuscript notes; offprint.
problems’
Offprint.
for
‘On
parity
(Semin.
A. Frohlich
NCUACS 153/3/07
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
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.
Photocopied typescript.
11pp typescript; offprint.
Oberwolfach
1980
(Lecture
notes
‘Algebraic number theory’. In Emmy Noether, a tribute to
her life and work (ed. J. Brewer and M. Smith), pp. 157-
163. New York: Marcel Dekker, 1981. Bibliog. no. 84
‘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
1975-1980;
‘Value distributions of symplectic root numbers’, Proc.
Lond. Math. Soc. 3rd ser. vol. 46 (1983), 83-99.
Bibliog.
no. 85
‘Galois module structure of algebraic integers’, Springer
Ergebn. 3rd ser. vol. 1 (1983), 1-258. Bibliog. no. 86
Correspondence re
Frdhlich’s
contribution,
35pp typescript draft; offprint.
1975-1986
A. Frohlich
NCUACS 153/3/07
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
These lectures were delivered at the University ofIllinois in
autumn 1981, when Frohlich was G.A. Miller Visiting
Professor there. See also D.7.
Bound volume.
Central Extensions, Galois Groups and Ideal Class Groups
of Number Fields, 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.81, C.82
Bound volumes.
2 folders.
Notes on lectures delivered in K6In 1982 (see D.11) and
Cambridge 1983.
Gauss’sche Summen. Notes of lectures taken by Kleinert,
Denninger, Everest. 2 vols. Mathematische Institut Kdéln,
1983. Bibliog. no. 90
(With C.J. Bushnell) ‘Non-Abelian congruence Gauss sums
‘Gauss sums’. In Sémin. Théorie des nombres, Paris,
1982-83 (Progr.
Bertin and C.
Goldstein), pp. 91-101. Boston, MA: Birkhauser, 1984.
Bibliog. no. 91.
Manuscript and typescript drafts; offprint.
Math.
51)
(ed.
M.-J.
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.
‘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.
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
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
See also D.24.
‘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.
Offprint.
A. Frohlich
NCUACS 153/3/07
Publications, C.1-C.125
‘Tame representation in base change’, Contemp. Math. vol.
86 (1989), 207-213. Bibliog. no. 99
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
Proof; photocopiedarticle.
‘Module defect and factorisability’, //linois J. Math. vol. 32
(1988), 407-421. Bibliog. no. 101
Offprint.
39pp typescript
Offprint.
Photocopiedoffprint.
Untitled draft beginning ‘Let K be a number field L finite
Galois extension of K’. Notlisted in Bibliog.
ca 1988
‘The genus class group |’, Sémin. Théorie des Nombres,
Bordeaux vol. 4 (1992), 97-111. Bibliog. no. 103
‘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
Copyof book.
(With M.J. Taylor) Algebraic number theory. Cambridge
University Press, 1991. Bibliog. no. 104
1991, 1995
A. Frohlich
NCUACS 153/3/07
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.
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,
39pp typescript draft
‘Corrected final’ draft, 23pp typescript
C.102, C.103
2 folders.
‘These
regulator
‘Il. Equivariant classgroups and Brauer groups’
61pp manuscript working, found with preceding material
but appears to be earlier in date.
This may berelated to
‘Generalisations of the Brauer group |’ (see C.45, C.45A).
Photocopied manuscript and typescript pages in Fréhlich’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.
Bibliog.
workings
Manuscript
connection
with
the
factorizability [...]
are
defined
computations
in
by AF and
See also C.44, C.110, E.106-E.111.
C.105-C.108
‘Galois modules and the functional equation’.
Notlisted in
ca 1995
A. Frohlich
NCUACS153/3/07
Publications, C.1-C.125
Manuscript and photocopied manuscript sections
C.106-C.108
Typescript drafts, three (slightly) different versions
3 folders.
‘Some remarks on wild extensions of number fields’, J.
reine angew. Math. vol. 495 (1998), 29-33.
Bibliog. no.
108
8pp photocopied manuscript draft; offprint.
(With C.T.C. Wall) ‘Equivariant Brauer groups’, Contemp.
Math. vol. 272 (2000), 57-71. Bibliog. no. 109
Qpp typescript; offprint.
See also C.44, C.45, C.102, C.103, E.106-E.111.
‘On the unit group normal number fields’
App typescript.
5 folders.
3 folders.
C.117-C.119
Draft beginning ‘Chapter 2 The cohomology theory E//*(X)’
Incomplete draft of ?book on ‘mathematical theory of
ostensive and consequently of empirical predicates’
Draft on groupoid spaces
‘Ali Frohlich’s review of Hassé Collected works’
C.112-C.116
5pp typescript so headed.
C4121, 6.122
A. Frohlich
NCUACS 153/3/07
Publications, C.1-C.125
43pp duplicated typescript.
2 folders.
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 Frdéhlich’s report.
Refereeing
1975, 1983,
n.d.
A. Frohlich
NCUACS 153/3/07
SECTION D
VISITS, CONFERENCES AND LECTURES, D.1-D.43
1956-1998,
n.d.
‘A reciprocity relation between pairs of quadratic forms’,
lecture given in Vienna, Austria, September 1956
6pp typescript resume.
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
(Fréhlich 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).
Visit to University of Arizona, January-June 1971
to
Frohlich
Visit to Israel, September-December 1978
Photocopy of newspaper cutting
visiting as National Science Foundation Fellow.
referring
List of participants receiving Science Research Council
support.
Research Symposium on Algebraic Number Theory, UK, 2-
12 September 1975
Programme.
Retirement Seminar, King’s College London, 12 June 1981
Frohlich was Royal
Research Professor.
Society-lsrael Academy Visiting
Letter from Royal Society re financial arrangements.
A. Frohlich
NCUACS 153/3/07
Visits, conferences and lectures, D.1-D.43
Visit to University ofIllinois at Urbana-Champaign, 1981-
1982
a
as
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 number of
other eminentvisiting scholars.
Professor
Miller
in
Announcement; programme for
lectures on Algebraic
Number Theory and Algebra (Frohlich is listed as lecturing
on ‘Galois module structure and the embedding problem’);
invitation to lecture at University of Chicago in February
1982 (invitation annotated by Fréhlich ‘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.
Frohlich
Zahlentheorie’.
lectured
on
‘Emmy Noethers
Beitrag
zur
Programme, invitation and correspondencearising.
Invitation, programme, photocopied manuscript lecture
notes.
Frohlich lectured on ‘Rings of algebraic integers as Galois
modules’.
American Mathematical Society 793rd Meeting, Bryn Mawr
College, Pennsylvania, USA, 16-17 March 1982
1981, 1982
Colloquium on Number Theory, Luminy, France, 28-June-3
July 1982
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
Fréhlich was basedat the University of Kdin.
A. Frohlich
NCUACS 153/3/07
Visits, conferences and lectures, D.1-D.43
Notice of three lectures at Kéln, ‘GauR’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 GauRsche
Summen fur einfache Algebren’); notice of lecture by
Frohlich on ‘Gauf&sche 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. MathematischeInstitut K6In, 1983 (see C.81,C.82).
Shorter correspondencere visits 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.
on
Conference
Mathematisches
Germany, 3-9 June 1984
Orders’
Forschungsinstitut,
and_
their
Applications,
Oberwolfach,
on
Algebraische
Programme.
Forschungsinstitut,
Programme, abstracts.
Zahlentheorie,
Oberwolfach,
Frohlich lectured on ‘Principal orders and arithmetic’.
Frohlich lectured ‘On Serre’s formula for the trace form’.
Conference
Mathematisches
Germany, 5-11 August 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 of local
principal orders’).
Visit to The Netherlands, December 1984
Rotterdam,
A. Frohlich
NCUACS 153/3/07
Visits, conferences and lectures, D.1-D.43
American Mathematical Society 818th Meeting, University
of Arizona, Tucson, USA, 12-13 April 1985
Annotated programme.
Mathematics
Germany, 14 June 1985
Colloquium,
University
of
Augsburg,
Programme.
Frohlich lectured on ‘Multiplikative und additive Galois-
Modul-Struktur’.
Pure Mathematics Workshop on Galois Modules and Zeta
Functions’, University of Exeter, 2-6 September 1985
Letter from
participants; programme.
R.W.K.
Odoni
re
arrangements;
list
of
Frohlich lectured on ‘Wild Galois module structure and
Gauss sums’.
Programme.
King’s College London,
16
connection
with
the
local
Programme and arrangements.
Frohlich lectured on ‘Galois module structure of units’.
Number Theory Seminar,
October 1985
Conference on Representation Theory and Number Theory
in
Langlands Conjecture’,
University of Augsburg, Germany, 8-14 December 1985
Summen und Langlands’sche Vermutung’.
Frohlich lectured on ‘Tame Deligne representations of Weil
groups, principal orders and base change’.
Colloquium to mark the 65th birthday of Herbert Benz,
University of KéIn, 25 January 1986
Programme.
Frohlich
lectured
on
‘Hauptordnungen,
Gauf’sche
A. Frohlich
NCUACS 153/3/07
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
Programme.
Frohlich gave lectures on ‘Galois module structure |’ and
‘Galois module structureII’.
Shorter correspondence re visits and conferences 1986-
1987
Society
Mathematical
American
Research
Institute on Representation Theory of Finite Groups and
Related Topics, University of California at Berkeley, 6-25
July
Sciences Research
Institute, Berkeley, California, 1986-1987.
to Mathematical
Summer
1986;
visit
Seminar on Number Theory, University of Bordeaux |, June
1987
Visit to China, autumn 1987
Letter re arrangements.
at S=0 and Galois
Théorie des Nombres,
Frohlich was Visiting Professor at the University of Beijing.
lectured on ‘L-functions
Frohlich
modules’. Published in Semin.
Bordeaux (1986-87), no. 32 (see also C.89).
Invitation; ‘Calculations and corrections in connection with
1987 Bordeaux paper’; copy of lecture as published.
1987, 1988
by
Meeting on arithmetic
University
and
Technology, 17-20 April 1988; NATO Advanced Studies
Institute
Banff,
Canada, 27 April-5 May 1988.
Shorter correspondencere visits and conferences 1988
in Number Theory and Applications,
Galois modules organised
Manchester
Institute
of
of
Science
A. Frohlich
NCUACS 153/3/07
Visits, conferencesand lectures, D.1-D.43
Visits to Germany, summer 1988
1987, 1988
Conferences
Oberwolfach
at
Mathematisches
Forschungsinstitut,
1987, 1988
Orders and their Applications, 29 May-4 June (Fréhlich
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,
Géttingen, 6-10 June (Fréhlich 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
by
Frdhlich
for
the
London
List of participants; annotated programme.
Programme,
report
Mathematical Society.
Frohlich lectured on ‘Genus Class-groups Factorizability
and Galois module structure’.
London Mathematical Society symposium on L-functions
and Arithmetic, University of Durham, 30 June-11 July
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.
Frohlich lectured on the theme of L-functions and Galois
modules.
Shorter correspondencere visits and conferences 1989
‘March,
Aaril
[...];
letter
from
A.. Frohlich
NCUACS 153/3/07
Visits, conferences and lectures, D.1-D.43
Colloquium at University of Augsburg, Germany, 24-25
November 1989
Invitation; programme.
Frohlich
lectured
zahlentheoretische
analytischer Methoden’.
on
Andwendung’
‘Galoismodulstruktur
-—
algebraischer
eine
und
Visit to McMaster University, Hamilton, Ontario, Canada,
March 1990
1989, 1990
list of Mathematics and Statistics Department
Invitation;
activities
for 19-23 March 1990 (Frdéhlich
listed as
lecturing on ‘Units in Abelian fields’ and giving a colloquium
on ‘Arithmetic Galois modules’).
is
Visit to Eidgenéssiche Technische Hochschule, Zurich,
Switzerland, June 1990
1989, 1990
Module
Newton
_Institute,
Programme.
of
Bordeaux
Invitation and letter re arrangements; letter re visit to
?University of K6In, June 1989.
Galoisiennes Arithmetiques,
24-28
Talence,
France,
|,
Outline of subjects to be covered (in French).
Galois
Isaac
University of Cambridge, 27 April 1993
Workshop,
Colloquium on Structures
University
September 1990.
structure’.
Conference on Integral Galois Structures, University of
Augsburg, Germany, 18-23 July 1993
Frohlich lectured on ‘Shadows and L-functions’.
Bound conferencereport.
Frohlich
lectured on
‘Strict
factorisability
in
additive
A. Frohlich
NCUACS 153/3/07
Visits, conferences and lectures, D.1-D.43
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,
Invitation and booking form; 11pp photocopied manuscript
lecture notes.
Frohlich lectured ‘On wild extensions of number fields’.
Programmefor unidentified two week meeting
Frohlich is listed as lecturing on ‘Hermitian structure of
algebraic integers’.
Contents of folder inscribed ‘Lecture’.
Transparenciesfor lecture ?0n number theory.
Manuscript draft of lecture beginning ‘A few years ago|
discussed some newinvariants of a discriminantal type — |
Manuscript notes labelled ‘Talks. Manitropic: factorizibility
(but also topics from the Springer and Birkhauser book)’.
have called them module conductors’.
A. Frohlich
NCUACS 153/3/07
SECTION E
CORRESPONDENCE,E.1-E.125
1950-2000
is
section
surviving
Frdhlich’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
problems with
mathematical workings, sometimes as
separate documents, and drafts of papers.
Although it
spans 1950-2000, the bulk dates from the 1970s-1990s.
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).
Brinkhuis, J.
Berge, A.-M.
1976-1980
See C.85.
Bayer, E.
Bayer was basedat the University of Geneva.
Includes photocopied manuscript draft ‘Isometric structures
with an irreducible characteristic polynomal’ by Bayer.
1984-2000
Includes manuscript draft of ‘Local Galois module structure
in the wild case’ by Berge.
Berge was based at the U.E.R. de Mathématiques et
d’Informatique,: University of Bordeaux |, Talence, France.
Brinkhuis was based at
Rotterdam, The Netherlands.
the Erasmus University
of
A. Frohlich
NCUACS 153/3/07
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’
Includes photocopied manuscript draft ‘Normal integral
bases and the Spiegelungssatz of Scholz’
Includes fragmentsofletters
2000, n.d.
Burns, D.
1992, 1993,
n.d.
Bushnell, C.J.
factorizations’,
‘On
classes’,
1980s-1996,
n.d.
Typescript drafts sent to Frohlich: ‘Adams operations and
integral Galois representations’, ‘On twisted Galois-Gauss
sums and canonical
arithmetically
realisable
‘A remark concerning arithmetical
associated orders’.
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 of Illinois 1972-1974 returned to King’s in 1974,
being appointed Professor of Pure Mathematics in 1990.
seventieth birthday’, 54pp typescript.
Chiefly re career, progress of research.
‘Hereditary
supercuspidal
representations of GLy [...] To Albrecht Frohlich on his
Gauss sums and_
orders,
CVs, research statements etc.
1980s, 1990s
Correspondence
1984, 1985,
n.d.
A. Frohlich
NCUACS 153/3/07
Correspondence, E.1-E.125
Correspondence
1987, 1988
Includes photocopied manuscript draft ‘Conductors of
primitive
sent to
Fréhlich for comment.
representations’
Bushnell
Galois
by
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.
Citation for Bushnell; undated letter from Frohlich
Cassels, J.W.S.
1972-1990
1966-1975
Chase, S.U.
Cassou-Nogués, P.
Chiefly on work in progress, with mathematical workings.
Cassou-Nogués was based at U.E.R. de Mathématiqueset
d'Informatique, University of Bordeaux |, Talence, France.
Although the letters are dated with the day and month, they
do not bear the year so cannotbe placed in chronological
order.
n.d.
Chinburg was Assistant Professor, then full Professor of
Mathematics at the University of Pennsylvania.
62pp manuscript on the local theory of resolvent and
related invariants.
Career, work in progress.
Chinburg, T.C.
1985-1989,
A. Frohlich
NCUACS 153/3/07
Correspondence, E.1-E.125
Cougnard, J.
1978-1982,
n.d.
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.
1983, n.d.
1963-1988
1990-1993,
1999
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.
1967-2000
1972-1973
the
time
of
writing
of
Galovich, S.P.
Galovich’s work on_
the
Includes correspondence re
projective class group.
At
Galovich was Professor
Mathematics at Carleton College, Northfield, Minnesota.
1975-1976
Includes 5pp draft typescript of introduction.
Collected works of H. Hasse.
Garbanati, D.
Geyer, W.-D.
A. Frohlich
NCUACS 153/3/07
Correspondence, E.1-E.125
Gras, G.
Progressof research.
Gras’s letters are in French.
Green, J.A.
Correspondence 1964 re problem from number theory.
Hall, P.
Hall was Sadlerian Professor of Pure Mathematics at
Cambridge.
1973-1974
1964, 1968,
1987
1968-1994
1958-1965
Hasse, H.
1965, 1974
E.32-E.36
Heilbronn, H.A.
1950-1976
Hasse was Professor of Mathematics at the University of
Hamburg.
Incoming letters only. In German. Correspondence 1965 is
chiefly re arrangementsfor visit to London.
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.
1950-1955
Correspondence of August 1955 includes manuscript
workings.
Heilbronn was Frdéhlich’s
Bristol.
Frohlich and J.W.S. Cassels wrote the Royal Society
Biographical Memoir of Heilbronn (see C.63).
supervisor at
Ph.D.
Correspondence and papers
Research in progress, social news(all incoming).
A. Fréhlich
NCUACS 153/3/07
Correspondence, E.1-E.125
Correspondence
including
criticism of paper by Frohlich to be submitted to the London
Mathematical Society.
progress,
research
re
in
1957, 1959
Correspondence re research in progress, including Abelian
fields and Artin L-functions.
Correspondence re research in 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.
Hsia, J.S.
Kani, E.
1966-1989
Holland, D.
1991-1993
of Mathematics at Ohio
State
Correspondencere problems of Ker A and Ker Z.
Hsia was Professor
University, USA.
Correspondence re move to McMaster University, Canada; _
draft papers on Chinburg’s Third Invariant.
1983-1988
Correspondence
Heilbronn’s collected works.
Kani was based at Harvard University.
of volume
of HA.
re
preparation
A. Frohlich
NCUACS 153/3/07
Correspondence,E.1-E.125
Kawamoto, F.
1983, 1984
Kawamoto was
Gakushuin University, Japan.
a
postgraduate
student
based
at
Includes ‘On normal integral bases of local fields’ by
Kawamoto sentto Frohlich for comment.
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.
Knus, M.A.
1970-1985
Knus was based at
Hochschule, Zurich, Switzerland.
the
Eidgendssiche Technische
the
at
Berlin
Progress of research, visits.
1965-1989,
n.d.
Progress of research.
Koch, H.
Kuroda, S.-N.
1954-1974
Deutsche Akademie der
the Akademie der
(later
Koch was based
Wissenschaften
zu
Wissenschaften der DDR), East Berlin, East Germany.
Research on epimorphism.
Progress of research, visit to London 1968-1969.
Lecouturier was a Belgian mathematician.
1967-1996
1965, 1966
Lecouturier, P.
A. Fréhlich
NCUACS 153/3/07
Correspondence, E.1-E.125
1966-1988
1978-1985,
n.d.
McCulloh, L.R.
McCulloh was Professor of Mathematics at University of
Illinois at Urbana-Champaign.
Chiefly re progress of research.
Macdonald, |.G.
Correspondence re working ‘Let O € Gal (Q cycl/Q)’.
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).
E.52-E.54
Martinet, J.
1970-1992
Curriculum vitae
Martinet was based at the U.E.R. de Mathématiques et
d’Informatique, University of Bordeaux |, Talence, France.
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).
1975-1984
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)
Correspondence re progress of research including paper
on W(x)=1, visits of Martinet and J. Queyrut to London and
Fréhlich to Bordeaux
1970-1974
A. Frohlich
NCUACS 153/3/07
Correspondence, E.1-E.125
Milnor, J.
Correspondence and papers re VV(D), including manuscript
workings by Frohlich.
Narkiewicz, W.
1964-1979
Narkiewicz was based at the
Poland.
University of Wroclaw,
Includes
answers.
questions on
normal
fields,
with
Frohlich’s
Nelson, A.M.
1981, 1984
Nelson was a postgraduate student of Fréhlich’s at King’s
College London in
late 1970s (Ph.D. ‘Monomial
Representations and Galois Module Structure’, see F.18).
He then moved to Macquarie University, Australia.
the
Ojanguren, M.
O.
Perlis, R.
Rédei, L.
Correspondence re work on Azumaya algebras.
Perlis was Professor of Mathematics at the Louisiana State
University, Baton Rouge, USA.
Ojanguren was based at the Battelle Advanced Studies
Centre, Geneva, Switzerland.
1954-1960
Includes a manuscript working by Perlis on the zeta
function.
Rédei was based at the Bolyai Mathematical Institute,
1979-1993
1983-1984
1972-1980
A. Frohlich
NCUACS 153/3/07
_ Correspondence, E.1-E.125
Szeged, Hungary.
Progress of research.
Incoming correspondenceonly, in German.
Reiner, I.
1971-1983
Reiner was based at the University of Illinois 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).
Correspondence and paperschiefly re work in progress on
Picent (A) — (C) and Picard groups, including comments
on drafts.
1971-1972
Ritter, J.
1980-1994
by
Ritter
on
‘On
the
integrality
of
Correspondence
1979, 1981,
1983
Most of the correspondenceis in German.
For most of the period covered by the correspondence
Ritter was based at the University of Augsburg, Germany.
Correspondence and papers, including manuscript and
photocopied manuscript workings by Frohlich, and text of
talk
group
representations’ by Ritter, referring to Frohlich’s work on
Galois module structure
1975-1992
Rocquette was Professor of Mathematics at the University
of Heidelberg, Germany.
Correspondenceonprogressof research
1980-1990
1991-1994
Rocquette, P.
A. Frohlich
NCUACS 153/3/07
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.
Rosenberg, A.
Correspondence re research problem.
Schertz, R.
Schertz was a mathematician based in KéIn, Germany.
Most of the correspondenceis in German.
1965-1996
1978-1981
EASE LCe
Serre, J.-P.
1960-1986
Muchof the incoming correspondenceisin French.
1960-1965
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.
Correspondence, including invitation to Serre to participate
in London Mathematical Society 1965 summer school on
algebraic number theory, and correspondencere areas to
be covered
1966-1971
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)
Correspondenceincluding 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
A. Frohlich
NCUACS 153/3/07
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_
attendance at meetings, visit to London etc.
Includes
photocopied manuscript workings by Serre, ‘Tate or “Stark”
(1978)’ and ‘La formule de Frohlich’
papers
work
re
1975-1978
Correspondence re work in progress, including Serre’s
comments on chapters 1-3 of Frohlich’s draft of ‘Galois
module structure of algebraic integers’ (see C.77)
1979-1981
Correspondencere workin progress
1982-1986
Snaith, V.
1984-1986
’) and
invitation
to
visit
Strooker, J.R.
Strooker was based at the University of Utrecht.
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.
number theory.
Chiefly
including London
Mathematical Society 1965 summer school on algebraic
re arrangements for
Tate was Professor of Mathematics at Harvard University.
1966-1980,
n.d.
1964-1976
1967-1971
Tate, J.T.
visits,
A. Fréhlich
NCUACS 153/3/07
Correspondence, E.1-E.125
E.82-E.90
Taussky-Todd, O.
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 Professorin 19771.
Taussky-Todd was Froéhlich’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 workin progress, and
visits
of fields
1957-1960
Frohlich’s planned visit in 1958 was cancelled as he was
unable to get an American visa.
visit
to the California
Correspondence re
Institute
Fellow
January-June 1962, work in progress on ideal matrices and
algebraic number theory
of Technology as Senior Research
Frdéhlich
of
1961-1965
1966-1971
1972-1973
1974-1975
See also D.2.
Correspondence re workin progress, including symmetry
and group rings, possible visits
Correspondence re work in progress, planned visit to
California Institute of Technology 1968
1979-1981
Correspondencere workin progress, visits and conference
attendance, including lecture by Taussky-Todd at King’s
College on ‘Some facts concerning integral
matrices’,
December 1974
Correspondence chiefly re visits, news of colleagues,
research plans
Correspondence re work on numbertheory and other work
1976-1978
A. Frohlich
NCUACS 153/3/07
Correspondence,E.1-E.125
in progress, visits, news of colleagues
Correspondence and papers
Includes photocopied manuscript note beginning, ‘There is
of course a large body of theory on orders in algebras over
numberfields and overlocal fields’, undated.
1984, 1987,
n.d.
re
obituary
Letter
London
Mathematical Society, copy of obituary in Notices of the
American Mathematical Society, August 1996, manuscript
notes by Frohlich
Taussky-Todd
for
of
E.91-E.97
Taylor, M.J.
1977-2000
London
1973-1976
Taylor was a postgraduate student of Froéhlich’s at King’s
College
Module
Structure of the Rings of Integers of /-extension’, 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.
ca 1997
E.93, E.94
1977-1979
Curriculum vitae
Correspondencere workin progress, including preparation
of papers, newsof colleagues
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.
n.d.
Includes photocopied manuscript ‘Comments on “Local
root numbers etc” ’ by Frohlich, annotated ‘Martin’ and
manuscript working beginning ‘For simplicity take G of
order Iq (The method extends to |'q without difficulty)’
annotated ‘File under Taylor’.
Correspondence and papers
1984, 1986,
2 folders.
A. Frohlich
NCUACS 153/3/07
E960E:97
Correspondence, E.1-E.125
preprints
Typescript
information:
characteristics’,
Arakelov Euler characteristics’
‘€-constants
‘Epsilon
by
and
constants
Martin
sent
to
Frohlich
for
Euler
equivariant
Arakelov
and
2 folders.
E.99-E.104
Ullom, S.V.
1974-1992
1967-1988
period
After a
Princeton, New Jersey,
University ofIllinois at Urbana-Champaign.
Institute
at the
USA,
for Advanced Study,
Ullom moved to
the
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,
Ullom’s
including
including
1975-1976
1972-1974
Ullom did come to London, supported by the University of
Illinois.
Correspondence and papers,
grant
application (unsuccessful) to spend sabbatical year 1976-
1977 at King’s College
Correspondence
__-Ullom’s
demonstration of ‘theorem for G a p-group, not necessarily
abelian, of order p wren oan correspondence re
Reiner, Ullom and Frdéhlich, ‘Class groups and Picard
groups of orders’, Proc. Lond. Math. Soc. 3rd ser. vol. 29
(1974) (see C.55), and other work in progress
1980-1981
Correspondencearising from Ullom’s sabbatical, work in
progress on Bernoulli numbers and tame extensions, news
of colleagues, visit to London 1979, etc.
Correspondencere workin progress including Gauss sums
1977-1979
A. Frohlich
NCUACS 153/3/07
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
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
Correspondence, chiefly re Brauer groups, and exchange
of drafts and offprints
Wall and Frohlich collaborated on a paper ‘Equivariant
Brauergroupsin algebraic number theory’, Bull. Soc. math.
Fr. vol. 25 (1971) (see C.44).
Includes ‘Construction of some basic categories’ by Wall,
8pp manuscript.
Correspondence, chiefly re Brauer groups and I-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)
Contemp. Math. vol. 272 (2000), see C.110.
Wall and Fréhlich 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.
A joint paper ‘Equivariant Brauer groups’ was publishedin
Correspondence, including progress on joint paper on
Brauer groups
1970-1971
‘Equivariant
Brauer groups
in
A. Frohlich
NCUACS 153/3/07
Correspondence, E.1-E.125
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 | wonder ifit will ever be completed’.
Correspondence and papers re workin progress, including
classgroups of 2-cyclotomic fields and Swan modules6 (r)
for 1 quaternion of order 2"
Also includes typescript draft of ‘Norms of units in group
rings (Corrigendum)’ by Wall.
Correspondence, including work on equivariant Brauer
groups
1976-1983,
2000, n.d.
Also includes undatedletters.
Ireland.
Weiss, A
Correspondencere Galois stable lattices.
Wehrfritz was based at Queen Mary College London.
Correspondencere problems in field theory.
Walter, C.D.
1975-1979
Wehrfritz, B.A.F.
1972-1981
Walter was based at Cambridge before taking up a postat
University College Dublin,
Fréhlich was an
examinerof Walter's Ph.D. thesis.
n.d.
Weiss was based at the University of Alberta, Edmonton,
Canada.
Wicke held a tutorial studentship in the King’s College
Bo. E 16
Wicke, G.
1967-1976,
A. Frohlich
NCUACS 153/3/07
Correspondence, E.1-E.125
Department
Mathematics
to
Germany he took up a post at the Free University of Berlin.
Fréhlich was external examiner for his Ph.D. thesis in
1975.
1962-1963.
return
On
Correspondence, chiefly re career
1967-1976
Photocopied
Resolventen’, annotated ‘File under Wicke’
manuscript
draft
‘Uber
allgemeine
Wielandt, H.
Includes correspondencere Fréhlich’s work on near-rings.
E.118-E.121
Wilson, S.M.J.
1973-ca 1994
ca 1994
1973-1976
Curriculum vitae
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.
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’
1979-1990
Includes typescript draft ‘Unsuccessful generalizations of
tame results to the wild case’, annotated ‘Wilson’.
Correspondence re work in progress and visits
Correspondence re work in progress
1977-1978
A. Frohlich
NCUACS 153/3/07
Correspondence, E.1-E.125
Zelinsky, D.
Zelinksy was based at Northwestern University, Evanston,
Illinois.
First name and unidentified
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
THESES
Thesesof Ph.D. students supervised or examinedby Frohlich.
1961-1990,
n.d.
1961-1989
King’s College London
1961-1982
‘Near-rings with descending chain conditions’ by Ronald
Robert Laxton, April 1961
Groups
‘Galois
September 1961
of
Polynomials’
by
Raimundo
Chela,
‘Topological
September 1964
Near Rings’
by
Veluppillai
Tharmaratnam,
‘Some invariants of algebras’ by Abraham Lue, November
1964
‘Some topics 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
1967
‘Some topics in the Theory of Orders’ by Michael Edward
Keating, 1967
‘Hermitian Forms over Algebras’ by Allan William McEvett,
A. Frohlich
NCUACS 153/3/07
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
‘Representations
Bushnell, February 1972
of 23-Graded
Groups’
by
Colin
John
‘On the K-theory of Twisted Group Rings’ by Stephen Mark
Johnson Wilson, March 1972
‘Varieties of Q-groups and associated functors’ by Joao
Candido de Antas Furtado Coelho, November 1972
‘The Brauer Group of Dimodule Algebras’ by F.W. Long, 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
Rings’ by Celia Ann Glass, July 1979
‘Monomial Representations and Galois Module Structure’ by
Adrian Maurice Nelson, May 1979
‘Realizable Classes in the Class Groups of Integral Group
A. Frohlich
NCUACS 153/3/07
Theses and examinations, F.1-F.33
‘Class Groups of Group Rings over Quadratic Number Fields
by Soroosh Homayouni 1982
University of Cambridge
1976, 1989
‘Class numberrelations in algebraic number fields’ by Colin
Donald Walter, April 1976
‘Factorisability, Group Lattices and Galois Module Structure’
by David Burns, December 1989
University ofIllinois
‘Genus Fields and central extensions of number fields’ by
Stephen Bruce Watt, 1983.
‘K-théorie algébrique et structure galoisienne des anneaux
F.24-F.28
University of Bordeaux |
1975-1986
‘Proprietes galoisiennes des anneaux d’entiers [...]’ by Jean
Cougnard, March 1975
‘Structure galoisienne des anneaux d’entiers’ by Philippe
Cassou-Nogués, October 1977
d’entiers’ by Jacques Queyrut, March 1980
‘Anneaux d’entiers et ordres associés’ by Anne-Marie Bergé,
April 1979
A. Frohlich
NCUACS 153/3/07
Theses and examinations, F.1-F.33
‘Sur la construction a noyau d’ordre p des p-extensions
galoisiennes’ by Richard Massy, March 1986
Research Students
Two lists of Frdhlich’s research students, one from online
‘Mathematics Genealogy Project’
http://genealogy.math.ndsu.nodak.edu/htmil/id.phtml?id=46030
(printed out May 2007).
F.30-F.33
EXAMINATIONS
1982-1990,
n.d.
Examination
calculations of answers.
and
test
papers,
some
with
Frdhlich’s
Cambridge Mathematical Tripos
Other tests and examinations
1982-1990,
Cambridge Mathematical Tripos
Cambridge Mathematical Tripos
n.d.
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
E.15
E.15
E.15
E.15
Ei
Es
See also F.26
E.15
D.15, E.4-E.7
BYOTT, N.P.
CALLAHAN, T.
BOLTJE, Dr
BONDI, Sir Hermann
BRINKHUIS, Jan
BROWN, Lawrence G.
BURNS, David
BUSHNELL, Colin John
E.9-E.14
See also F.12
E.15
A.23
E.68
B:5636.0/7, E30
See also F.22
CALIFORNIA INSTITUTE OF TECHNOLOGY
E.20
CASSOU-NOGUES, Philippe,
CASSELS, John William Scott (‘lan’)
E.16
See also C.36
E15
D.2
E.36
A.36
CARLETON UNIVERSITY
CHAPMAN, Robin J.
See NOGUES
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
E.17A
B.56, B.57, E.18
A.8, E.19
See also F.24
E.36
E.20
E24
E24
E.80
E.21
E22
E23
FRESNEL, Jean
FURUTA, Yoshiomi
GEYER, W.-D.
GOLD, R. (‘Bob’)
E.23
E.23
A.11
E.23
E.24
E.25
FRIEDMAN, Eduardo
GARBANATI, Dennis
GALOVICH, StevenP.
A.8, A.9,A.11, A.13, A.14
FROHLICH, Sorrel Ruth Tamar
FROHLICH (née BROOKS), (Evelyn) Ruth
E.28
GREEN, JamesAlexander (‘Sandy’)
GORMAN, Howard E.
£29
E29
E29
E.29
E2/,
GOLDHABER, Jack
GOLDMAN, O.
GRAS, Georges
D.8, E.26
A. Frohlich
NCUACS 153/3/07
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
Index of correspondents
E.29
E.39
E.30
Eon
See also E.26
A.19
E-39
A.24, E.32-E.36
See also C.63
D.10
E.39
Ss,
E.39
HSIA, John S
HUQ, Syed Afzal-ul
E.38
E.42
D.34, E.39
JARDEN, Moshe
JEHNE, Wolfram
KAHN, Bruno
KANI, Ernst
E:39
E.39
IWASAMA,Kenkichi
E.39
See also F.5
E.43
E.46
See also F.9
KAWAMOTO, Fuminori
E.46
E.40
E.41
E.46
KETTERER, Brian
KLEIMAN, Howard
KNESER, Martin
KNUS, Max Albert
KAPLANSKY, Irving
D.23, E.46
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.
LI Delang
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
LINFOOT, Edward Hubert
McEVETT, Allan William
D.12, E.52-E.54
A.19
E.48
E.48
E.55
E.56
MARTINET, Jacques
MILNOR, John
LUBIN, Jonathan D.
LUTHAR, Indar Singh
McCULLOH, Leon R.
MACDONALD, lan G.
A.11, E.49
E.50
E51
See also F.8
A.11,A.14, A.28, A.34, D.29, D.314
LONDON MATHEMATICAL SOCIETY
See also F.25
NOGUES,Philippe, CASSOU-
E57
See also F.18
E.51
Ald) E17
NARKIEWICZ, Wladyslaw
NELSON, Adrian Maurice
NEUMANN, Peter M.
A. Frohlich
NCUACS 153/3/07
Index of correspondents
ODONI, Robert W.K.
D118; E:59
OJANGUREN, M.
OPOLKA,Hans
ORDE, H.L.S.
OXFORD UNIVERSITY PRESS
PATTERSON, S.J. (‘Paddy’)
PERLIS, Robert
POITOU, Georges
QUEYRUT,J.
RADO, Richard
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
RAJWADE, A.R.
REDEI, L.
RITTER, Jurgen
REINER, Irving
REMMERT,R.
RIEHM, Carl
E.63, E.64
C.77
D.9, E.69
REICHARDT, Hans
ROSENBERG, Alex
ROCQUETTE, Peter
ROGERS, C. Ambrose
C101; D.32\E.65; E66
E.80
A.8, A.24, A.25, A.33, D.5
SCHERTZ, Reinhard
E.67
E.36
A.31
SCHARLAU, Winfrid
ROTH, Klaus F.
ROYAL SOCIETY
SEMPLE, Jack G.
E50; E66
E.80
E.70
A. Frohlich
NCUACS 153/3/07
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
E.71-E.77
E.80
E.80
D.33, E.78
A.22
= 19
A.14, E.80
See DYER
E.81
E.82-E.90
D.26, E.91-E.97
See also F.17
THARMARATNAM, Veluppillai
E.98
See also F.3
See TAUSSKY-TODD
THE TIMES
THOMPSON, John G.
TODD, John
ULLOM, Stephen V.
E.63, E.99-E.104
TODD, Olga TAUSSKY-
THOMPSON, Richard B.
A.37
A.13
E.98
E.98
E.83
THOMAS, Charles Benedict
UNIVERSITY COLLEGE OF NORTH STAFFORDSHIRE
A.21
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
UNIVERSITY OF LEICESTER
UNIVERSITY OF BRISTOL
A.19, A.35
A.22
D.7
D.30
UNIVERSITY OF IOWA
Index of correspondents
A. Frohlich
NCUACS 153/3/07
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.
A.32
A.23
E.36
E.105
E.105
e122
E.106-E.111
EAt2
See also F.21
E22
E.122
WATSON, G.L.
e122
BalilS E116
WEISS, Al.
WHARPLES, George
WICKE, Gunter
WIELANDT, Helmut
WILES, Andrew
WATT, Stephen Bruce
WEHRFRITZ, Bert A.F.
E.113
E.114
E122
WILSON, Stephen Mark Johnson
Eei22
See also E.104, F.23
E.124
ZEEMAN, Sir (Erik) Christopher
E.118-E.121
See also F.13
YAHYA, Saiyed Mohammed
E117
E22
EA22
E123
E.123
WRIGHT,David J.
ZELINSKY, Daniel
A. Frohlich
NCUACS 153/3/07
ZINK, W.-W.
Index of correspondents
