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.