Chern subrings

TL;DR

This paper investigates the relationship between Chern classes and the Chow ring of classifying spaces for certain algebraic groups, showing limitations when p-torsion is present in homology.

Contribution

It demonstrates that for simply-connected semisimple complex groups with p-torsion in homology, Chern classes do not generate the Chow ring of their classifying space.

Findings

Chern classes fail to generate the Chow ring when p-torsion exists

The result applies to simply-connected semisimple complex algebraic groups

Highlights limitations of Chern class generation in algebraic topology

Abstract

Let p be an odd prime. We show that for a simply-connected semisimple complex linear algebraic group, if its integral homology has p-torsion, the Chern classes do not generate the Chow ring of its classifying space.