On the Problem of Mixed-Tateness of the Motives of G-Varieties

TL;DR

This paper investigates the motives of specific G-varieties, demonstrating they are mixed-Tate under certain stabilizer conditions, with applications and examples illustrating the scope and limitations of these results.

Contribution

It establishes conditions under which motives of G-varieties are mixed-Tate, extending previous work on G-bundles and providing new insights into their structure.

Findings

Motives of certain G-varieties are mixed-Tate under stabilizer conditions.

Examples show limitations of the mixed-Tate property.

Applications demonstrate relevance to algebraic geometry.

Abstract

Building on earlier work concerning the motives of $G$-bundles, we study the structure of motives associated with certain classes of $G$-varieties. In particular, we show that the corresponding motives lie within the category of mixed-Tate motives, under certain condition on the stabilizers. We further discuss some applications and provide some examples to illustrate the limitations.