A functor D_crys is constructed that links prismatic F-crystals to filtered Frobenius crystals and, in the Fontaine-Laffaille range, induces an equivalence of categories.
Filtered F-crystals on Shimura varieties of abelian type
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abstract
In this paper, we define and construct canonical filtered $F$-crystals with $G$-structure over the integral models for Shimura varieties of abelian type at hyperspecial level defined by Kisin. We check that these are related by $p$-adic comparison theorems to the usual lisse sheaves, and as an application we also use this to show that the Galois representations generated from the $p$-adic \'etale cohomology of Shimura varieties with nontrivial coefficient sheaves are crystalline, at least in the case of proper abelian type Shimura varieties.
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An integral analogue of Fontaine's crystalline functor
A functor D_crys is constructed that links prismatic F-crystals to filtered Frobenius crystals and, in the Fontaine-Laffaille range, induces an equivalence of categories.