Proves the Pappas-Rapoport conjecture on canonical integral models of Hodge-type Shimura varieties with quasi-parahoric level at p, shows uniformization by integral local Shimura varieties, and proves the Kisin-Pappas conjecture on local model diagrams.
Éléments de géométrie a lgébrique. III. Étude cohomologique des faisceaux cohérents. I
4 Pith papers cite this work. Polarity classification is still indexing.
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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.
Establishes a representability criterion for v-sheaf modifications of formal schemes and applies it to parahoric level structures on local shtukas, yielding local representability of integral models of local Shimura varieties under hyperspecial levels.
Constructs integral models for Shimura varieties of abelian type with parahoric level at odd primes that are étale locally isomorphic to local models.
citing papers explorer
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On a conjecture of Pappas and Rapoport
Proves the Pappas-Rapoport conjecture on canonical integral models of Hodge-type Shimura varieties with quasi-parahoric level at p, shows uniformization by integral local Shimura varieties, and proves the Kisin-Pappas conjecture on local model diagrams.
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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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Relative representability and parahoric level structures
Establishes a representability criterion for v-sheaf modifications of formal schemes and applies it to parahoric level structures on local shtukas, yielding local representability of integral models of local Shimura varieties under hyperspecial levels.
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Integral models of Shimura varieties with parahoric level structure, II
Constructs integral models for Shimura varieties of abelian type with parahoric level at odd primes that are étale locally isomorphic to local models.