Cohomologie cohérente et représentations Galoisiennes

In this paper, we show how the ideas introduced in Scholze (On torsion in the cohomology of locally symmetric varieties, prépublication, 2015) apply to the study of coherent cohomology of Siegel varieties, and more generally of Shimura varieties of Hodge type. The principal result asserts that higher cohomology classes are p-adic limits of cuspidal modular forms. This enables us to associate Galois representations to some automorphic representations appearing in the coherent cohomology of Shimura varieties.