Comparison between étale p-adic and crystalline cohomology on some Shimura varieties

We consider an integral model X at a prime p of a Shimura variety of PEL type having good reduction. This variety is associated to a reductive group G. I will explain how we can associate to Zp-representations of this group two kinds of sheaves on X : étale sheaves on the generic fiber, and crystals on the special fiber. I will then show how we can compare the cohomology groups of these two kinds of sheaves.