Papers by Dave Benson


Back to Dave Benson's Preprint Archive


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Comments and corrections for the books and papers of Dave Benson

Latest version: Sept 2010.


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Modules for elementary abelian groups and hypersurface singularities

MSRI, 2013.


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Modules of constant Jordan type and a conjecture of Rickard

To appear in J. Algebra.


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Representations of elementary abelian p-groups and vector bundles

This is a very preliminary version of a book on representations of elementary abelian p-groups, especially concentrating on modules of constant Jordan type and the vector bundles on projective space associated with them. I'm aware that there are a lot of imperfections in the manuscript. Updates will be frequent.


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Modules of constant Jordan type with small non-projective part

To appear in Algebras and Representation Theory.


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Modules for elementary abelian p-groups

Proceedings of ICM, Hyderabad, India 2010, Volume II, 113-124. World Scientific 2011.


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Modules of constant Jordan type with one non-projective block

Algebras and Representation Theory 13 (2010), 315-318.


Scan of Thesis: pdf; Summary: dvi

The Simple Group J4

Ph D Thesis, Cambridge, 1982.
Thesis supervisor: Prof. J.G. Thompson.


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Periodic resolutions for certain finite groups

International Electronic Journal of Algebra 6 (2009), 46-64.


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An algebraic model for chains on ΩBGp^

Transactions of the AMS 361 (2009), 2225-2242.


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Resolutions over symmetric algebras with radical cube zero

J. Algebra 320 (2008), 48-56.


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Idempotent kG-modules with injective cohomology

Journal of Pure and Applied Algebra 212 (2008), 1744-1746.


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On the regularity conjecture for the cohomology of finite groups

Proc. Edinburgh Math. Soc. 51 (2008), 273-284.


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Commutative algebra and duality in the cohomology of groups

Lecture notes for four lectures given at the ICTP, Trieste, 2004.


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On the classifying space and cohomology of Thompson's sporadic simple group

To John Thompson on the occasion of his 70th birthday

Finite Groups 2003: Proceedings of the Gainesville Conference on Finite Groups, March 6-12, 2003.
Edited by Chat Ho, Peter Sin, Pham Tiep and Alex Turull. Walter de Gruyter (2004), 47-57.


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Dickson invariants, regularity and computation in group cohomology

Illinois J. Math. 48 (1) (2004), 171-197.


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Commutative algebra in the cohomology of groups

Three lectures given at the opening conference for the MSRI program in commutative algebra, Sept 9-13, 2002.
Trends in Commutative Algebra, MSRI Publications, Volume 51 (2004), 1-50.


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Phantom maps and purity in modular representation theory, III

J. Algebra 248 (2002), 747-754.


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The nucleus, and extensions between modules for a finite group

Proceedings of the Nineth International Conference on Representations of Algebras (ICRA9), Beijing, August 21-Sept 1 2000, Second Volume, Beijing Normal University Press (2002), 145-155.


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Modules with injective cohomology, and local duality for a finite group

New York J. Math. 7 (2001), 201-215.

Needs yinit font


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Infinite dimensional modules for finite groups

Three lectures given at the Euroconference Workshop on Infinite Length Modules, Bielefeld, 1998. Appeared in "Infinite Length Modules", Trends in Mathematics, Birkhäuser Verlag (2000), 251-272.


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Flat modules over group rings of finite groups

Algebras and Representation Theory 2 (1999), 287-294.


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Problem session for the Seattle 1996 AMS Summer Research Institute Conference on Cohomology, Representation and Actions of Finite Groups.
Edited by Dave Benson.

Proc. Symp. Pure Math. 63 (1998), 519-532.


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Cohomology of sporadic groups, finite loop spaces, and the Dickson invariants

Proceedings of the 1994 Durham Conference on Geometry and Cohomology in Group Theory, ed. Kropholler, Niblo and Stöhr. London Math. Soc. Lecture Note Series, 252 (1998),10-23.


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The Brauer homomorphism

One page article, Encyclopædia of Mathematics Supplement Volume I, Editor-in-Chief M. Hazewinkel, Kluwer Academic Publishers (1997), 151.

Needs xypic fonts


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Complexity and varieties for infinite groups, I

J. of Algebra 193 (1997), 260-287.


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Complexity and varieties for infinite groups, II

J. of Algebra 193 (1997), 288-317.


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Infinite dimensional modules for a finite group

Representation Theory of Finite Groups, Proceedings of the 1995 Ohio State Conference, ed. Ron Solomon, de Gruyter (1997), 11-17.


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Decomposing the complexity quotient category

Math. Proc. Camb. Phil. Soc. 120 (1996), 589-595.


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Fusion in compact Lie groups

Quart. J. Math. 47 (1996), 261-268.


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Stably splitting BG

Survey article, Bull. AMS 33 (1996), 189-198.


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Cohomology of modules in the principal block of a finite group

New York Journal of Mathematics 1 (1995), 196-205.


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(Warning: the TeX form of this document has some missing lines in the pictures. For a more complete document, see the journal)

Conway's group Co3 and the Dickson invariants

Manuscripta Mathematica 85 (1994), 177-193

Needs xypic fonts


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The image of the transfer

Archiv der Mathematik 61 (1993), 7-11


(Not available in TeX form for copyright reasons)

Polynomial Invariants of Finite Groups

(v + 126 pp.)

LMS Lecture Notes in Mathematics 190, CUP, 1993


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(Warning: the TeX form of this document has some missing lines in the pictures. For a more complete document, see the Springer Lecture Notes volume)

Resolutions and Poincaré duality for finite groups

In: Proceedings of the June 1990 Barcelona conference on Homotopy and Group Cohomology. Springer Lecture Notes in Mathematics 1509, Springer-Verlag, 1992.


(Not available in TeX form for copyright reasons)

Representations and Cohomology, Vol. I: Basic representation theory of finite groups and associative algebras

(xi + 224 pp.)

Cambridge Studies in Advanced Mathematics 30, CUP 1991

MR 92m:20005, ZB 718.20001

Paperback edition, CUP 1998.

MR 99f:20001


(Not available in TeX form for copyright reasons)

Representations and Cohomology, Vol. II: Cohomology of groups and modules

(x + 278 pp.)

Cambridge Studies in Advanced Mathematics 31, CUP 1991

MR 93g:20099, ZB 731.20001

Paperback edition, CUP 1998.

MR 99f:20001


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Cyclic homology and path algebra resolutions

Math. Proc. Camb. Phil. Soc. 106 (1989), 57-66


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Projective modules for the group of the twenty-seven lines on a cubic surface

Comm. in Algebra 17 (5) (1989), 1017-1068

See the comment in the comments file (top of this page) about the main theorem of this paper.


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Spin modules for symmetric groups

J. London Math. Soc. (2) 38 (1988), 250-262


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Some remarks on the decomposition numbers for the symmetric groups

The Arcata Conference on Representations of Finite Groups, Proc. Symp. Pure Math. AMS 47, Part 1 (1987), 381-394


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Representation rings of finite groups

(Two lectures given at the 1985 Durham Symposium on the Representations of Algebras) Representations of Algebras, Durham 1985. LMS Lecture Notes in Mathematics 116, 181-199, CUP, 1986


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Modules for finite groups: representation rings, quivers and varieties

(Three lectures given at the Fourth International Conference on the Representations of Algebras) Representation Theory II, Groups and Orders, Ottawa 1984. Springer Lecture Notes in Mathematics 1178, 1-24. Springer-Verlag, Berlin/New York 1986


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Brauer trees for 12M22

J. of Algebra 95 (1985), 398-408


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Some recent trends in modular representation theory

Proceedings of the group theory year at Rutgers, CUP 1985, 249-259


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Lambda and psi operations on Green rings

J. of Algebra 87 (1984), 360-367


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Modular representation theory: New trends and methods

Springer Lecture Notes in Mathematics 1081, Springer-Verlag, Berlin/New York 1984


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The Loewy structure of the projective indecomposable modules for A8 in characteristic 2

Comm. in Algebra 11 (13) (1983), 1395-1432


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The Loewy structure of the projective indecomposable modules for A9 in characteristic 2

Comm. in Algebra 11 (13) (1983), 1433-1453


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Extended (6 page) index for Cartan and Eilenberg, Homological Algebra, PUP, 1956. Compiled by Dave Benson, 2003.


See also
Adem and Benson
Balmer, Benson and Carlson
Benson and Carlson
Benson, Carlson and Rickard
Benson, Carlson and Robinson
Benson, Chebolu, Christensen and Mináč
Benson and Cohen
Benson and Conway
Benson and Crawley-Boevey
Benson and Doty
Benson, Erdmann and Holloway
Benson, Erdmann and Mikaelian
Benson and Evens
Benson, Feit and Howe
Benson and Feshbach
Benson and Gnacadja
Benson and Goodearl
Benson and Green
Benson and Greenlees
Benson, Grodal and Henke
Benson and Habegger
Benson, Iyengar and Krause
Benson and Kessar
Benson and Krause
Benson, Krause and Schwede
Benson and Kropholler
Benson, Kumjian and Phillips
Benson, Lemire, Mináč and Swallow
Benson and Lim
Benson and Linckelmann
Benson and Martin
Benson and Nakano
Benson and Parker
Benson and Pevtsova
Benson and Smith
Benson and Webb
Benson and Wheeler
Benson and Wilkerson
Benson and Witherspoon
Benson and Wood