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

TL;DR

This paper proves the Kottwitz conjecture for certain unitary PEL-type Rapoport-Zink spaces by establishing a local Langlands correspondence and an averaging formula relating cohomology to this correspondence.

Contribution

It extends existing results to construct a local Langlands correspondence for unramified unitary groups and proves the Kottwitz conjecture for these groups.

Findings

Constructed a local Langlands correspondence for unramified unitary groups.

Proved an averaging formula linking cohomology to the Langlands correspondence.

Established the Kottwitz conjecture for the studied groups.

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.