Stratifying modular representations of finite groups

• 成果类型: Article
• 署名作者: Benson, David J.; Iyengar, Srikanth B.; Krause, Henning
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.174.3.6
• 发表日期: 2011
• 页码: 1642-1683
• 关键词: smashing subcategories; COHOMOLOGY; localization; HOMOLOGY; spectrum; Respect

摘要

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.