$D$-Elliptic Sheaves and Uniformisation

TL;DR

This paper presents an analytic uniformisation of certain varieties over function fields, analogous to Shimura varieties' uniformisation, providing new insights into their structure at the infinite place.

Contribution

It introduces a uniformisation method for Laumon, Rapoport, and Stuhler varieties over function fields, extending the analogy with Shimura varieties.

Findings

Provides an explicit uniformisation at the infinite place.

Establishes a parallel between function field varieties and classical Shimura varieties.

Enhances understanding of the structure of these varieties in the function field setting.

Abstract

An analytic uniformisation of the varieties of Laumon, Rapoport and Stuhler at the infinite place is presented. This can be seen as the function field analog to the uniformisation of Shimura varieties classifying Abelian varieties with large endomorphism rings.