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arXiv · 2104.05912

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

Alexander Bertoloni Meli·Kieu Hieu Nguyen
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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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BibTeXRIS

Alexander Bertoloni Meli, Kieu Hieu Nguyen. 2021-04-13. The Kottwitz conjecture for unitary PEL-type Rapoport--Zink spaces. https://arxiv.org/abs/2104.05912

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