Stratification of Derived Categories of Tate Motives

TL;DR

This paper classifies the localizing tensor ideals of derived categories of mixed Tate motives over algebraically closed fields, establishing their stratification and introducing a new technique for transferring stratification via Brown--Adams representability.

Contribution

It provides a complete classification of localizing tensor ideals in these categories and develops a novel method for transferring stratification between categories.

Findings

Categories are stratified in the sense of Barthel, Heard, and Sanders.

Introduces a new technique for transporting stratification using Brown--Adams representability.

Enhances understanding of the structure of derived categories of Tate motives.

Abstract

We classify the localizing tensor ideals of the derived categories of mixed Tate motives over certain algebraically closed fields. More precisely, we prove that these categories are stratified in the sense of Barthel, Heard and Sanders. A key ingredient in the proof is the development of a new technique for transporting stratification between categories by means of Brown--Adams representability, which may be of independent interest.