Geodesic
Finiteness of cohomology groups of stacks of shtukas as modules over Hecke algebras, and applications
Épijournal de Géométrie Algébrique, Tome 4 (2020)

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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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     author = {Xue, Cong},
     title = {Finiteness of cohomology groups of stacks of shtukas as modules over {Hecke} algebras, and applications},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     volume = {4},
     year = {2020},
     doi = {10.46298/epiga.2020.volume4.5550},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2020.volume4.5550/}
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Xue, Cong. Finiteness of cohomology groups of stacks of shtukas as modules over Hecke algebras, and applications. Épijournal de Géométrie Algébrique, Tome 4 (2020). doi: 10.46298/epiga.2020.volume4.5550

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