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.