Relative equivariant motives and modules
Algebraic Geometry
2021-01-20 v3 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1609.06929,
title = {Relative equivariant motives and modules},
author = {Baptiste Calmès and Alexander Neshitov and Kirill Zainoulline},
journal= {arXiv preprint arXiv:1609.06929},
year = {2021}
}
Comments
25pp; This is a substantially revised and reorganized version. Several proofs were revised and simplified. Examples added