Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

Cohomology with integral coefficients of stacks of shtukas

Résumé

We construct the cuspidal cohomology groups of stacks of shtukas with $\mathbb Z_{\ell}$-coefficients and prove that they are $\mathbb Z_{\ell}$-modules of finite type. We prove that the cohomology groups with compact support of stacks of shtukas with $\mathbb Z_{\ell}$-coefficients are modules of finite type over a Hecke algebra with $\mathbb Z_{\ell}$-coefficients. As an application, we prove that the cuspidal cohomology groups with $\mathbb Q_{\ell}$-coefficients are equal to the Hecke-finite cohomology groups with $\mathbb Q_{\ell}$-coefficients defined by V. Lafforgue.

Dates et versions

hal-03866688 , version 1 (22-11-2022)

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Cong Xue. Cohomology with integral coefficients of stacks of shtukas. 2022. ⟨hal-03866688⟩
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