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, equiva-lently all) modules. One application is a proof of the telescope conjecture in this context. Others include new proofs of the tensor product theo-rem 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.