Une suite spectrale de Hochschild–Serre pour l'uniformisation de Rapoport–ZinkAn Hochschild–Serre spectral sequence for the Rapoport–Zink uniformization

In this Note we announce results concerning the first part of a programme intending to generalize the articles [5,7] and thus construct local Langlands correspondences for groups other than GL_n (for example, quasisplit unitary groups) inside the ? adic cohomology of Rapoport–Zink spaces. The method consists in comparing the cohomology of these local objects with that of global objects: Shimura varieties. For this we generalize the spectral sequences constructed in [5] and [4]. A part of these results is quoted in [6]. To cite this article: L. Fargues, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 739–742.