  Let $X$ be an integral model at a prime $p$ of a Shimura variety of PEL type
having good reduction, associated to a reductive group $G$. To $\mathbb{Z}_p$
reprsententations of the group $G$ can be associated two kinds of sheaves :
crystals on the special fiber of $X$, and locally constant \'etale sheaves on
the generic fiber. We establish a comparison between the cohomology of these
two kinds of sheaves.
