Congruences automorphes et torsion dans la cohomologie d’un système local d’Harris-Taylor

Abstract

This paper is a part of a sequence of works of the author to understand the ℤ l ¯-cohomology of some simple unitary Shimura varieties. We use previous results of the author on the ℚ l ¯-cohomology groups, as well as the description of the entire filtration of stratification of the perverse sheaf of vanishing cycles at a split place of those Shimura varieties, to produce on one part torsion classes in some of the initial terms of a spectral sequence which calculate the cohomology groups of the Shimura variety and, on a another part, some automorphic congruences.