The Kottwitz conjecture for unitary PEL-type Rapoport--Zink spaces
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Publication:6365139
DOI10.1515/CRELLE-2022-0077arXiv2104.05912WikidataQ123221897 ScholiaQ123221897MaRDI QIDQ6365139
Alexander Bertoloni Meli, Kieu Hieu Nguyen
Publication date: 12 April 2021
Abstract: In this paper we study the cohomology of PEL-type Rapoport-Zink spaces associated to unramified unitary similitude groups over 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.
Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Langlands-Weil conjectures, nonabelian class field theory (11S37) Linear algebraic groups over local fields and their integers (20G25)
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