Stratification and \(\pi \)-cosupport: finite groups
We introduce the notion of \(\pi \)-cosupport as a new tool for the stable module category of a finite group scheme. In the case of a finite group, we use this to give a new proof of the classification of tensor ideal localising subcategories. In a sequel to this paper, we carry out the corresponding classification for finite group schemes.
KeywordsCosupport Stable module category Finite group scheme Localising subcategory Support Thick subcategory
Mathematics Subject ClassificationPrimary 16G10 Secondary 20C20 20G10 20J06
Part of this article is based on work supported by the National Science Foundation under Grant No. 0932078000, while DB, SBI, and HK were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the 2012–2013 Special Year in Commutative Algebra. The authors thank the Centre de Recerca Matemàtica, Barcelona, for hospitality during a visit in April 2015 that turned out to be productive and pleasant. SBI and JP were partly supported by NSF Grants DMS-1503044 and DMS-0953011, respectively. We are grateful to Eric Friedlander for comments on an earlier version of this paper.
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