Genus formula for modular curves of $D$-elliptic sheaves

TL;DR

This paper derives a genus formula for modular curves associated with D-elliptic sheaves and demonstrates that their reductions reach the Drinfeld-Vladut bound as the discriminant degree increases.

Contribution

It provides a new genus formula for these modular curves and shows their reductions attain the Drinfeld-Vladut bound in the limit.

Findings

Genus formula for modular curves of D-elliptic sheaves

Reductions attain the Drinfeld-Vladut bound as discriminant degree grows

Enhances understanding of asymptotic properties of these curves

Abstract

We prove a genus formula for modular curves of $D$-elliptic sheaves. We use this formula to show that the reductions of modular curves of $D$-elliptic sheaves attain the Drinfeld-Vladut bound as the degree of the discriminant of $D$ tends to infinity.