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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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. I

# FROHLICH, Albrecht v2

Published: 16 January, 2024 Author: admin