# Un cas PEL de la conjecture de Kottwitz

## TL;DR

This paper proves the Kottwitz conjecture for certain basic unramified unitary PEL type Rapoport-Zink spaces by studying related Shimura varieties and their cohomology.

## Contribution

It provides a proof of the Kottwitz conjecture for a new class of Rapoport-Zink spaces using geometric methods on Shimura varieties.

## Key findings

- Confirmed the Kottwitz conjecture for basic simple unramified unitary PEL Rapoport-Zink spaces.
- Established geometric links between Shimura varieties and Rapoport-Zink spaces.
- Enhanced understanding of the cohomology of these moduli spaces.

## 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).