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Some torsion classes in the Chow ring and cohomology of $BPGL_n$ (1901.10090v3)

Published 29 Jan 2019 in math.AG and math.AT

Abstract: In the integral cohomology ring of the classifying space of the projective linear group $PGL_n$ (over $\mathbb{C}$), we find a collection of $p$-torsions $y_{p,k}$ of degree $2(p{k+1}+1)$ for any odd prime divisor $p$ of $n$, and $k\geq 0$. If in addition, $p2\nmid n$, there are $p$-torsion classes $\rho_{p,k}$ of degree $p{k+1}+1$ in the Chow ring of the classifying stack of $PGL_n$, such that the cycle class map takes $\rho_{p,k}$ to $y_{p,k}$. We present an application of the above classes regarding Chern subrings.

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