Un cas PEL de la conjecture de Kottwitz
[A PEL case of the Kottwitz conjecture]
Annales de l'Institut Fourier, Volume 73 (2023) no. 6, pp. 2239-2304.

The Kottwitz conjecture describes the cohomology of basic Rapoport–Zink spaces using local Langlands correspondences. In this paper, via geometrical studies of some Kottwitz-type Shimura varieties, we prove this conjecture for basic simple unramified unitary PEL type Rapoport–Zink spaces of signature (1,n-1).

La conjecture de Kottwitz décrit la cohomologie des espaces de Rapoport–Zink basiques à l’aide des correspondances de Langlands locales. Dans cet article, par voie globale via l’étude de la géométrie de certaines variétés de Shimura de type Kottwitz, on prouve cette conjecture pour des espaces de Rapoport–Zink de type PEL unitaires non ramifiés simples basiques de signature (1,n-1).

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Accepted:
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DOI: 10.5802/aif.3577
Classification: 11F70, 11F80, 11F85, 11G18, 20C08
Mot clés : Espaces de Rapoport–Zink, Conjecture de Kottwitz, Formes automorphes.
Keywords: Rapoport–Zink spaces, Kottwitz conjecture, Automorphic forms.
Nguyen, Kieu Hieu 1

1 University of Münster (WWU) Einsteinstrasse, 62. 48149 Münster (Germany)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Nguyen, Kieu Hieu. Un cas PEL de la conjecture de Kottwitz. Annales de l'Institut Fourier, Volume 73 (2023) no. 6, pp. 2239-2304. doi : 10.5802/aif.3577. https://aif.centre-mersenne.org/articles/10.5802/aif.3577/

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