Stratifying modular representations of finite groups

View/ Open
Date
2008-03-20MFO Scientific Program
Research in Pairs 2008Series
Oberwolfach Preprints;2008,20Author
Benson, David J.
Iyengar, Srikanth B.
Krause, Henning
Metadata
Show full item recordOWP-2008-20
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.