%0 Journal Article
%T Equivariant crystalline cohomology and base change
%A Elmar Grosse-Kl£¿nne
%J Mathematics
%D 2014
%I arXiv
%X Given a perfect field $k$ of characteristic $p>0$, a smooth proper $k$-scheme $Y$, a crystal $E$ on $Y$ relative to $W(k)$ and a finite group $G$ acting on $Y$ and $E$, we show that, viewed as virtual $k[G]$-module, the reduction modulo $p$ of the crystalline cohomology of $E$ is the de Rham cohomology of $E$ modulo $p$. On the way we prove a base change theorem for the virtual $G$-representions associated with $G$-equivariant objects in the derived category of $W(k)$-modules.
%U http://arxiv.org/abs/1408.3353v1