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On the generic part of the cohomology of local and global Shimura varieties

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arxiv 2106.10602 v1 pith:AKGHZNGE submitted 2021-06-20 math.NT math.AG

Teruhisa Koshikawa This is my paper · ORCID
classification math.NTmath.AG
keywords cohomologyshimuravarietiesgenericlocalpartvanishingalternative
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Using the work of Fargues-Scholze, we prove a vanishing theorem for the generic unramified part of the cohomology of local Shimura varieties of general linear groups. This gives an alternative approach to vanishing results of Caraiani-Scholze for the cohomology of unitary Shimura varieties.

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  1. Categorical local Langlands and torsion classes of some Shimura varieties

    math.NT 2025-05 conditional novelty 6.0 of 10

    For GL_n over unramified p-adic fields, the paper proves the strongly generic part of the categorical local Langlands conjecture with F_l coefficients and derives Harris-Viehmann type identities and torsion vanishing ...

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