Un cas PEL de la conjecture de Kottwitz

2019/03/27 by Kieu Hieu Nguyen, Nguyen, Kieu Hieu
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1903.11505

openalex publication_date 2019/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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).

Related

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• Correspondances de Langlands locales dans la cohomologie des espaces de Rapoport-Zink
• On the Kottwitz conjecture for local shtuka spaces
• Cohomology of the basic unramified PEL unitary Rapoport-Zink space of signature (1,n-1)
• An averaging formula for the cohomology of PEL-type Rapoport--Zink spaces