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

epiga:5550 - Épijournal de Géométrie Algébrique, June 17, 2020, Volume 4 - https://doi.org/10.46298/epiga.2020.volume4.5550
Finiteness of cohomology groups of stacks of shtukas as modules over Hecke algebras, and applicationsArticle

Authors: Cong Xue

    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.


    Volume: Volume 4
    Published on: June 17, 2020
    Accepted on: April 1, 2020
    Submitted on: June 6, 2019
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Number Theory,Mathematics - Representation Theory
    Funding:
      Source : OpenAIRE Graph
    • Global Methods in the Langlands Program; Funder: European Commission; Code: 714405

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