Constructs functorial Igusa stacks for Hodge-type Shimura varieties, yielding a sheaf on Bun_G that controls cohomology and proves compatibility with the semisimple local Langlands correspondence of Fargues-Scholze while establishing torsion vanishing for proper cases.
Katz, Slope filtration of F -crystals , Journ\' e es de G \' e om\' e trie A lg\' e brique de R ennes ( R ennes, 1978), V ol
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Slope numbers, domino numbers, and Hodge-Witt numbers from Hodge-Witt and crystalline cohomology are derived invariants in positive characteristic, restricting Hodge numbers of derived equivalent varieties.
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Igusa Stacks and the Cohomology of Shimura Varieties
Constructs functorial Igusa stacks for Hodge-type Shimura varieties, yielding a sheaf on Bun_G that controls cohomology and proves compatibility with the semisimple local Langlands correspondence of Fargues-Scholze while establishing torsion vanishing for proper cases.
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Derived invariants from topological Hochschild homology
Slope numbers, domino numbers, and Hodge-Witt numbers from Hodge-Witt and crystalline cohomology are derived invariants in positive characteristic, restricting Hodge numbers of derived equivalent varieties.