An almost polynomial subring of the Chow ring and Cohomology of $BPGL_n$

Xing Gu

Published 2020-12-01Version 1

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 $\mathbb{C}$, and explain a way in which this computation might play a role in the period-index problem. In addition, we show that the Chow rings of $BPGL_n$ is not generated by the Chern classes of linear representations of $PGL_n$.