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Stratification and \(\pi\)-cosupport: finite groups. (English) Zbl 1483.20088

Summary: 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.

MSC:

20J06 Cohomology of groups
16G10 Representations of associative Artinian rings
20C20 Modular representations and characters
20G10 Cohomology theory for linear algebraic groups
14L15 Group schemes
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