Mod p classification of Shimura F-crystals

Details Mod p classification of Shimura F-crystals Mod p classification of Shimura F-crystals

2003-04-02

arxiv.org/abs/math/0304030v7

Mathematics

Number Theory

Final version 55 pages. To appear in Math. Nachr. (44 pages in the journal's format)

Scientific paper

Let $k$ be an algebraically closed field of positive characteristic $p$. We first classify the $D$-truncations mod $p$ of Shimura $F$-crystals over $k$ and then we study stratifications defined by inner isomorphism classes of these $D$-truncations. This generalizes previous works of Kraft, Ekedahl, Oort, Moonen, and Wedhorn. As a main tool we introduce and study Bruhat $F$-decompositions; they generalize the combined form of Steinberg theorem and of classical Bruhat decompositions for reductive groups over $k$.

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