Models of Shimura varieties in mixed characteristic

this paper, we will attempt to use this fact to study models in mixed characteristic of these Shimura varieties. To this end, a "local p-adic analogue" of a Shimura variety is introduced in the following way. We start with a principally polarized abelian scheme X over the ring W of Witt vectors of the algebraic closure F p of a finite field. We fix a tensor product TDR (X=W ) of DeRham cohomology groups of X and their duals, twisted to make the weight equal to 0, and we choose a class ¸ 2 Fi