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

2025/12/21 by Somayeh Habibi, Habibi, Somayeh
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2512.18645

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.

Citations

• On The Motivic Leray-Hirsch Theorem For Pure Tate Fibre Bundles
• A remark on a result of Huber and Kahn
• Some Motivic Remarks On The Moduli Stacks Of global G-Shtukas And Their Local Models
• On the Motive of a Fibre Bundle and its Applications
• Mixed Tate motives over \Z
• Families of rationally simply connected varieties over surfaces and torsors for semisimple groups
• Homogeneous spaces and equivariant embeddings
• Noncommutative geometry and motives: the thermodynamics of endomotives
• Seiberg-Witten Theory and Random Partitions
• Les variétés sur le corps à un élément
• The Chow motive of semismall resolutions

Related

• On The Motive of G-bundles
• The mixed Tate property of reductive groups
• An introduction to mixed Tate motives
• Groups of order p³ are mixed Tate
• Equivariant motives and geometric representation theory. (with an appendix by F. Hörmann and M. Wendt)