Stratification for module categories of finite group schemes

TL;DR

This paper classifies tensor ideal localising subcategories in the stable module category of all representations of a finite group scheme over a field of positive characteristic, including infinite dimensional cases.

Contribution

It provides a comprehensive classification of these subcategories and explores their implications for the structure and support behavior in the stable module category.

Findings

Classification of tensor ideal localising subcategories

Analysis of support and cosupport behavior

Applications to the structure of the stable module category

Abstract

The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning the structure of the stable module category and the behavior of support and cosupport under restriction and induction are presented.