The étale cohomology of the general linear group over a finite field and the Dickson algebra

Abstract

Let $p\ne \ell$ be primes. We study the étale cohomology $H_{\text{ét}}^{\ast }\left({\mathrm{BGL}}_n\right({\mathbb{F}}_{p^s});\mathbb{Z}/\ell )$ by using the stratification methods from Molina-Rojas and Vistoli. To compute this cohomology, we use the Dickson algebra and the Drinfeld space.