Cyclic coverings of the projective line by Mumford curves in positive characteristic

TL;DR

This paper investigates the structure of cyclic coverings of the projective line by Mumford curves in positive characteristic, explicitly determining their defining equations over complete discrete valuation fields.

Contribution

It provides a method to explicitly find the defining equations of degree p cyclic coverings by Mumford curves in positive characteristic, extending previous work from characteristic zero.

Findings

Derived explicit equations for cyclic coverings by Mumford curves

Extended understanding of rigid analytic geometry in positive characteristic

Connected previous characteristic zero results to positive characteristic cases

Abstract

We study the rigid analytic geometry of cyclic coverings of the projective line. We determine the defining equation of a cyclic covering of degree $p$ of the projective line by a Mumford curve over a complete discrete valuation field of positive characteristic $p$. Previously, Bradley studied that of any degree over a non-archimedean local field of characteristic zero.