(Co)stratification of stable categories for infinite groups

TL;DR

This paper classifies key subcategories within the stable module category for infinite groups, specifically for LH F groups, and develops techniques applicable to other infinite group categories.

Contribution

It provides a classification of localising tensor ideal and colocalising hom-closed subcategories for the stable module category of LH F groups, introducing new methods for infinite groups.

Findings

Classification of subcategories for LH F groups

Development of techniques for other infinite group categories

Framework applicable to broader classes of infinite groups

Abstract

We classify the localising tensor ideal and colocalising hom-closed subcategories of the stable module category for $\mathrm{LH}\mathfrak{F}$ groups. Along the way we develop techniques to provide similar classifications for other categories of infinite groups.