On hyperelliptic modular curves over function fields

TL;DR

This paper proves the finiteness of hyperelliptic modular curves of D-elliptic sheaves over function fields and provides a complete classification in odd characteristic.

Contribution

It establishes finiteness results and classifies hyperelliptic modular curves over function fields, advancing understanding of their structure in algebraic geometry.

Findings

Finiteness of hyperelliptic modular curves over function fields.

Complete classification in odd characteristic.

Identification of conditions for hyperelliptic curves.

Abstract

We prove that there are only finitely many modular curves of $D$-elliptic sheaves over $\mathbb{F}_q(T)$ which are hyperelliptic. In odd characteristic we give a complete classification of such curves.