
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.
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