A distinguished subring of the Chow ring and cohomology of $BPGL_n$

TL;DR

This paper identifies a specific subring within the Chow ring and cohomology of the classifying space of PGL_n, revealing new structural insights and implications for the period-index problem.

Contribution

It determines a particular subring of the Chow ring and cohomology of BPGL_n and shows that the Chow ring is not generated by Chern classes of linear representations.

Findings

Identified a distinguished subring of the Chow ring and cohomology of BPGL_n.

Showed that the Chow ring of BPGL_n is not generated by Chern classes of linear representations.

Explained potential implications for the period-index problem.

Abstract

We determine a subring of the Chow ring and the cohomology of $BPGL_n$, the classifying space of the projective linear group of degree $n$ over complex numbers, and explain a way in which this computation might play a role in the period-index problem. In addition, we show that the Chow ring of $BPGL_n$ is not generated by the Chern classes of linear representations of $PGL_n$.