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.
On a conjecture of Pappas and Rapoport
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We prove a conjecture of Pappas and Rapoport about the existence of ''canonical'' integral models of Shimura varieties of Hodge type with quasi-parahoric level structure at a prime $p$. For these integral models, we moreover show uniformization of isogeny classes by integral local Shimura varieties, and prove a conjecture of Kisin and Pappas on local model diagrams.
fields
math.NT 3years
2024 3verdicts
UNVERDICTED 3representative citing papers
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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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.