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Mod \(p\) classification of Shimura \(F\)-crystals. (English) Zbl 1264.11053
For an algebraically closed field \(k\) of characteristic \(p >0\), the author classifies \(D\)-truncations mod \(p\) of Shimura \(F\)-crystals over \(k\). These are used to study different stratifications of special fibers of integral canonical models of Shimura varieties of Hodge type in the mixed characteristic case. The stratifications are defined by inner automorphism classes of the \(D\)-truncations. The main tool introduced is the Bruhat \(F\)-decomposition, generalizing the classical Bruhat decomposition for reductive groups over \(k\).

MSC:
11G18 Arithmetic aspects of modular and Shimura varieties
14F30 \(p\)-adic cohomology, crystalline cohomology
14L30 Group actions on varieties or schemes (quotients)
14G35 Modular and Shimura varieties
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