# Cohomology of finite general linear groups

Cohomology of finite general linear groups

Speaker: David Sprehn, University of Washington

Abstract:
I will introduce the problem of computing the mod-$p$ cohomology of $GL_n(k)$ for $k$ the finite field of order $p^r$, then describe how to construct a new class in (lowest possible) degree $r(2p-3)$, and show it's nonzero (when $n\leq p$) by restricting to a subgroup of commuting regular unipotent matrices.  I’ll first explain how the number $r(2p-3)$ comes out of the invariant theory of finite fields. Lastly, I’ll describe what’s necessary to generalize the result to finite groups of Lie type.