Stratifying modular representations of finite groups

David J. Benson, Srikanth B. Iyengar, Henning Krause

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context. Others include new proofs of the tensor product theorem and of the classification of thick subcategories of the finitely generated modules which avoid the use of cyclic shifted subgroups. Along the way we establish similar classifications for differential graded modules over graded polynomial rings, and over graded exterior algebras.
Original languageEnglish
Pages (from-to)1643-1684
Number of pages42
JournalAnnals of Mathematics
Volume174
Issue number3
DOIs
Publication statusPublished - 2011

Fingerprint

Modular Representations
Finite Group
Module
Tensor Product
Exterior Algebra
Graded Module
Graded Ring
Graded Algebra
Polynomial ring
Finitely Generated
Telescope
Classify
Subgroup
Closed
Theorem

Keywords

  • local cohomology
  • local-global principle
  • modular representation theory
  • stable module category
  • stratification
  • telescope conjecture

Cite this

Stratifying modular representations of finite groups. / Benson, David J. ; Iyengar, Srikanth B. ; Krause, Henning.

In: Annals of Mathematics, Vol. 174, No. 3, 2011, p. 1643-1684.

Research output: Contribution to journalArticle

Benson, DJ, Iyengar, SB & Krause, H 2011, 'Stratifying modular representations of finite groups', Annals of Mathematics, vol. 174, no. 3, pp. 1643-1684. https://doi.org/10.4007/annals.2011.174.3.6
Benson, David J. ; Iyengar, Srikanth B. ; Krause, Henning. / Stratifying modular representations of finite groups. In: Annals of Mathematics. 2011 ; Vol. 174, No. 3. pp. 1643-1684.
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