Nous exposons dans cette Note les résultats constituant la première partie d'un programme visant à généraliser les articles [5,7] et ainsi construire des correspondances de Langlands locales pour d'autres groupes que GLn (par exemple des groupes unitaires quasidéployés) dans la cohomologie ℓ-adique des espaces de Rapoport–Zink. La méthode consiste à comparer la cohomologie de ces objets locaux à celle d'objets globaux : les variétés de Shimura. Pour cela nous généralisons les suites spectrales établies dans [5] et [4]. Une partie de ces résultats est mentionnée dans [6].
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 GLn (for example, quasisplit unitary groups) inside the ℓ 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].
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@article{CRMATH_2002__334_9_739_0,
author = {Laurent Fargues},
title = {Une suite spectrale de {Hochschild{\textendash}Serre} pour l'uniformisation de {Rapoport{\textendash}Zink}},
journal = {Comptes Rendus. Math\'ematique},
pages = {739--742},
publisher = {Elsevier},
volume = {334},
number = {9},
year = {2002},
doi = {10.1016/S1631-073X(02)02340-3},
language = {fr},
}
Laurent Fargues. Une suite spectrale de Hochschild–Serre pour l'uniformisation de Rapoport–Zink. Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 739-742. doi : 10.1016/S1631-073X(02)02340-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02340-3/
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