De Rham F-gauges and Shimura varieties

2024/03/04 by Xu Shen, Shen, Xu
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2403.01899

Abstract

We study F-gauges for de Rham cohomology of smooth algebraic varieties in characteristic p. Applying to good reductions of Shimura varieties of Hodge type, we recover the Ekedahl-Oort stratifications by constructing universal de Rham F-gauges with G-structure. We also study the cohomology of de Rham F-gauges on these varieties. In particular, in the PEL type case and when the weights of the flat automorphic vector bundles are p-small, we determine the F-gauge structure on their de Rham cohomology by the associated dual BGG complexes.

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