Thick subcategories of the bounded derived category of a finite group

TL;DR

This paper provides a new, more direct proof for classifying tensor ideal thick subcategories in derived categories of finite group representations and artinian complete intersection rings, avoiding infinite constructions.

Contribution

It introduces a novel proof technique that simplifies the classification of thick subcategories without relying on infinite methods.

Findings

Classification of tensor ideal thick subcategories achieved

Proof applies to both finite group representations and artinian complete intersection rings

Avoids the use of infinite constructions in the proof

Abstract

A new proof of the classification for tensor ideal thick subcategories of the bounded derived category, and the stable category, of modular representations of a finite group is obtained. The arguments apply more generally to yield a classification of thick subcategories of the bounded derived category of an artinian complete intersection ring. One of the salient features of this work is that it takes no recourse to infinite constructions, unlike the previous proofs of these results.