Comparaison entre cohomologie cristalline et cohomologie étale $p$-adique sur certaines variétés de Shimura
Abstract
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 étale sheaves on the generic fiber. We establish a comparison between the cohomology of these two kinds of sheaves.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2007
- DOI:
- 10.48550/arXiv.0704.1347
- arXiv:
- arXiv:0704.1347
- Bibcode:
- 2007arXiv0704.1347R
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14G35 14F30