Comparaison entre cohomologie cristalline et cohomologie étale $p$-adique sur certaines variétés de Shimura

Details Comparaison entre cohomologie cristalline et cohomologie étale $p$-adique sur certaines variétés de Shimura Comparaison entre cohomologie cristalline et cohomologie étale $p$-adique sur certaines variétés de Shimura

2007-04-11

arxiv.org/abs/0704.1347v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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