Sur la torsion dans la cohomologie des variétés de Shimura de Kottwitz-Harris-Taylor

Abstract

When the level at $l$ of a Shimura variety of Kottwitz-Harris-Taylor is not maximal, its cohomology with coefficients in a ${\overline{\mathbb{Z}}}_l$-local system isn't in general torsion free. In order to prove torsion freeness results of the cohomology, we localize at a maximal ideal $\mathfrak{m}$ of the Hecke algebra. We then prove a result of torsion freeness resting either on $\mathfrak{m}$ itself or on the Galois representation ${\overline{\rho }}_{\mathfrak{m}}$ associated to it. Concerning the torsion, in a rather restricted case than the work of Caraiani-Scholze, we prove that the torsion doesn't give new Satake parameters systems by showing that each torsion cohomology class can be raised in the free part of the cohomology of a Igusa variety.

in French

References in corpus (3)

• Weight cycling and Serre-type conjectures for unitary groups
• p-adic Hodge-theoretic properties of étale cohomology with mod p coefficients, and the cohomology of Shimura varieties
• Congruences automorphes et torsion dans la cohomologie d'un système local d'Harris-Taylor

Cited by in corpus (3)

• Shimura varieties at level ${\Gamma }_1(p^{\infty })$ and Galois representations
• Ihara's lemma and level rising in higher dimension
• A $p$-adic approach to the existence of level-raising congruences