The Kottwitz conjecture for unitary PEL-type Rapoport--Zink spaces

2021/04/13 by Alexander Bertoloni Meli, Meli, Alexander Bertoloni, Kieu Hieu Nguyen +1 · 1 citation
Mathematics · #11G18 #11S37 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.AG #math.NT #math.RT #msc:11G18 #msc:11S37

paper · pdf · doi:10.48550/arxiv.2104.05912

57 pages, comments welcome

openalex publication_date 2021/04/13 · arxiv created 2021/06/30 · arxiv updated 2021/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the cohomology of PEL-type Rapoport-Zink spaces associated to unramified unitary similitude groups over \Q_p in an odd number of variables. We extend the results of Kaletha-Minguez-Shin-White to construct a local Langlands correspondence for these groups and prove an averaging formula relating the cohomology of Rapport-Zink spaces to this correspondence. We use this formula to prove the Kottwitz conjecture for the groups we consider.

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