Chow rings of quasi-split geometrically almost simple algebraic groups

TL;DR

This paper extends the computation of Chow rings from split algebraic groups to quasi-split, geometrically almost simple groups using equivariant conormed Chow rings, providing new tools for understanding their algebraic geometry.

Contribution

It introduces equivariant conormed Chow rings and computes the Chow ring for quasi-split geometrically almost simple algebraic groups, extending classical results.

Findings

Chow ring of quasi-split groups computed

Introduction of equivariant conormed Chow rings

Extension of classical split group results

Abstract

We compute the Chow ring of a quasi-split geometrically almost simple algebraic group assuming the coefficients to be a field. This extends the classical computation for split groups done by Kac to the non-split quasi-split case. For the proof we introduce and study equivariant conormed Chow rings, which are well adapted to the study of quasi-split groups and their homogeneous varieties.