La cohomologie des espaces de Lubin-Tate est libre

Abstract

This article is the entire version, that is with coefficients in the ring of integers of a local field, of my last paper at inventiones. The principal result is the freeness of the cohomology groups of the Lubin-Tate tower. The strategy is to study the process of saturation in the construction of the filtration of stratification of Harris-Taylor systems local and of the perverse sheaf of vanishing cycles of some unitary Shimura variety. In this new version we use the mirabolic representation and we study the l-torsion of the cockerel between $p$ and $p+$ Harris-Taylor perverse sheaves.Comment: 42 pages, in Frenc