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.
Koshikawa, On the generic part of the cohomology of local and global Shimura varieties , arXiv:2106.10602 , preprint, (2021)
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Locally analytic vectors in the completed cohomology of GL_n over CM fields admit infinitesimal characters determined by Sen operators of associated Galois representations, confirming the Dospinescu-Paškūnas-Schraen conjecture in this case.
A result is established about the non-generic cohomology of certain compact unitary Shimura varieties for good p, extending Boyer's work via a different approach in the Fargues-Scholze context.
Establishes arithmetic level raising for quaternionic unitary Shimura varieties of degree four at ramified primes, using supersingular locus descriptions related to Siegel threefolds.
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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Infinitesimal characters for the completed cohomology of $\mathrm{GL}_n$ over CM fields
Locally analytic vectors in the completed cohomology of GL_n over CM fields admit infinitesimal characters determined by Sen operators of associated Galois representations, confirming the Dospinescu-Paškūnas-Schraen conjecture in this case.
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On the non-generic part of cohomology of compact unitary Shimura varieties of signature $(1,n)$
A result is established about the non-generic cohomology of certain compact unitary Shimura varieties for good p, extending Boyer's work via a different approach in the Fargues-Scholze context.
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Arithmetic level raising for certain quaternionic unitary Shimura variety
Establishes arithmetic level raising for quaternionic unitary Shimura varieties of degree four at ramified primes, using supersingular locus descriptions related to Siegel threefolds.