The Langlands-Kottwitz approach for some simple Shimura Varieties

TL;DR

This paper applies the Langlands-Kottwitz method to compute local factors of the zeta-function for specific Shimura varieties and proves a related conjecture by Haines and Kottwitz.

Contribution

It demonstrates how the Langlands-Kottwitz approach can be used for particular Shimura varieties and confirms a conjecture in this context.

Findings

Determined semisimple local factors of the Hasse-Weil zeta-function.

Proved a conjecture of Haines and Kottwitz for these cases.

Validated the effectiveness of the Langlands-Kottwitz method in this setting.

Abstract

We show how the Langlands-Kottwitz method can be used to determine the semisimple local factors of the Hasse-Weil zeta-function of certain Shimura varieties. On the way, we prove a conjecture of Haines and Kottwitz in this special case.