Cohomologie coherente et representations Galoisiennes
ResumeDans cet article, on montre comment les idees introduites dans l'article Scholze (On torsion in the cohomology of locally symmetric varieties, prepublication, 2015) s'appliquent a l'etude de la cohomologie coherente des varietes de Siegel, et plus generalement des varietes de Shimura de type Hodge. Le resultat principal affirme que les classes de cohomologie coherente superieure sont des limites p adique de formes modulaires cuspidales. Ceci permet dans certains cas d'associer des representations galoisiennes a des formes automorphes apparaissant dans la cohomologie coherente de varietes de Shimura.AbstractIn this paper, we show how the ideas introduced in Scholze (On torsion in the cohomology of locally symmetric varieties, prepublication, 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.