Stratification and $\pi$-cosupport: Finite groups

TL;DR

This paper introduces $\pi$-cosupport as a new method to analyze the stable module category of finite groups, providing a novel proof for classifying tensor ideal localising subcategories, with extensions to finite group schemes.

Contribution

It presents the concept of $\pi$-cosupport and applies it to classify tensor ideal localising subcategories in the stable module category of finite groups.

Findings

New proof of classification of tensor ideal localising subcategories

Introduction of $\pi$-cosupport as a tool

Extension of classification to finite group schemes

Abstract

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.