Relative Equivariant Motives and Modules

Baptiste Calmès (1) , Alexander Neshitov , Kirill Zainoulline

1 LML - Laboratoire de Mathématiques de Lens

We introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. We show that the motivic decomposition type of a versal flag variety depends on the direct sum decomposition type of the parabolic module. To do this we use localization techniques of Kostant-Kumar in the context of generalized oriented cohomology as well as the Rost nilpotence principle for algebraic cobordism and its generic version. As an application, we obtain new proofs and examples of indecomposable Chow motives of versal flag varieties.

Domaines: Géométrie algébrique [math.AG]; K-théorie et homologie [math.KT]

Baptiste Calmès, Alexander Neshitov, Kirill Zainoulline. Relative Equivariant Motives and Modules. 2020. ⟨hal-02942574⟩