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Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations

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arxiv 1507.05922 v1 pith:EA4JXLDV submitted 2015-07-21 math.NT

George Boxer This is my paper · ORCID
classification math.NT
keywords coherentcohomologycongruencesshimuratorsionvarietiesadaptedautomorphic
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We introduce a method for producing congruences between Hecke eigenclasses, possibly torsion, in the coherent cohomology of automorphic vector bundles on certain good reduction Shimura varieties. The congruences are produced using some "generalized Hasse invariants" adapted to the Ekedahl-Oort stratification of the special fiber.

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  1. On the generic part of the cohomology of non-compact unitary Shimura varieties

    math.NT 2019-09 accept novelty 8.0 of 10

    Generic mod ℓ cohomology of non-compact unitary Shimura varieties is concentrated above the middle degree, and fibers of the compactified Hodge-Tate period map are compactified Igusa varieties.

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