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Finiteness of cohomology groups of stacks of shtukas as modules over Hecke algebras, and applications

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arxiv 1811.09513 v3 pith:DPT7DASY submitted 2018-11-23 math.AG math.NTmath.RT

Cong Xue This is my paper · ORCID
classification math.AGmath.NTmath.RT
keywords automorphiccohomologycompactformsgroupsheckemodulesshtukas
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In this paper we prove that the cohomology groups with compact support of stacks of shtukas are modules of finite type over a Hecke algebra. As an application, we extend the construction of excursion operators, defined by V. Lafforgue on the space of cuspidal automorphic forms, to the space of automorphic forms with compact support. This gives the Langlands parametrization for some quotient spaces of the latter, which is compatible with the constant term morphism.

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  1. A toy model for the Drinfeld-Lafforgue shtuka construction

    math.AG 2019-08 conditional novelty 7.0 of 10

    In a Betti/topological setting, applying categorical and 2-categorical traces to a Hecke action yields universal shtukas, excursion operators, and an S=T identity.

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