English

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

R2 v1 2026-06-22T15:57:47.645Z