Cohomology with integral coefficients of stacks of shtukas

Abstract

We construct the cohomology groups with compact support of stacks of shtukas with ${\mathbb{Z}}_{\ell }$-coefficients. We construct the cuspidal cohomology groups and prove that they are ${\mathbb{Z}}_{\ell }$-modules of finite type. We prove that the cohomology groups 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. We also state the Eichler-Shimura relations for cohomology groups with ${\mathbb{Z}}_{\ell }$-coefficients and prove the compatibility of the excursion operators and the constant term morphisms.

Added the Eichler-Shimura relations for cohomology groups with ${\mathbb{Z}}_{\ell }$-coefficients

References in corpus (1)

• Cycles on Shimura varieties via geometric Satake

Cited by in corpus (1)

• Coherent sheaves on the stack of Langlands parameters