Points on Shimura varieties over finite fields: the conjecture of Langlands and Rapoport

TL;DR

This paper refines the Langlands-Rapoport conjecture and proves it for many Shimura varieties, including the first proof for those of PEL-type, advancing understanding in arithmetic geometry.

Contribution

It provides an improved conjecture statement and establishes its validity for a broad class of Shimura varieties, notably PEL-type.

Findings

Proof of the conjecture for a large class of Shimura varieties

First proof of the original conjecture for PEL-type Shimura varieties

Enhanced understanding of the structure of Shimura varieties over finite fields

Abstract

We state an improved version of the conjecture of Langlands and Rapoport, and we prove the conjecture for a large class of Shimura varieties. In particular, we obtain the first proof of the (original) conjecture for Shimura varieties of PEL-type.