Stratifying modular representations of finite groups

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.

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Authors

David J. Benson

Institute of Mathematics
University of Aberdeen
King's College
Aberdeen AB24 3UE
Scotland
UK

Srikanth B. Iyengar

Department of Mathematics
University of Nebraska
Lincoln, NE 68588-0130

Henning Krause

Faculty of Mathematics
Universität Bielefeld
PO Box 100 131
D-33501 Bielefeld
Germany