On the Chow rings of classifying spaces for classical groups

TL;DR

This paper demonstrates how the stratification method can unify the computation of Chow rings for classifying spaces of various classical groups, extending previous results in algebraic geometry.

Contribution

It introduces a unified approach using stratification to compute Chow rings of classifying spaces for classical groups, building on Vezzosi's method.

Findings

Unified stratification method applies to multiple classical groups

Provides a systematic way to compute Chow rings

Extends known computations to new cases

Abstract

We show how the stratification method, introduced by Vezzosi in his study of PGL_3, provides a unified approach to the known computations of the Chow rings of the classifying spaces of GL_n, SL_n, Sp_n, O_n and SO_n.