Stratifying integral representations via equivariant homotopy theory

TL;DR

This paper demonstrates that the derived category of R-linear representations of a finite group G can be stratified using equivariant homotopy theory, leading to a classification of certain tensor ideals.

Contribution

It introduces a new approach to stratify derived categories of group representations over regular rings using equivariant homotopy theory.

Findings

Derived category of R-linear G-representations is stratified for any regular ring R.

Classifies localizing tensor ideals of R-linear G-representations with projective modules.

Provides a framework connecting equivariant homotopy theory with representation theory.

Abstract

We prove that the derived category of $R$-linear representations of a finite group $G$ is stratified for any regular commutative ring $R$. As an application, we obtain a classification of localizing tensor ideals of ordinary $R$-linear $G$-representations whose underlying $R$-module is projective.