Moduli of Galois p-covers in mixed characteristics

TL;DR

This paper constructs a proper moduli stack for degree p Galois covers of twisted stable curves, generalizing classical covers to mixed characteristic settings with finite flat group schemes.

Contribution

It introduces a new moduli stack framework for degree p covers over twisted stable curves in mixed characteristics, extending existing theories.

Findings

Defines a proper moduli stack for degree p covers in mixed characteristic.

Establishes the stability and torsor structure over twisted stable curves.

Provides a foundation for further study of Galois covers in arithmetic geometry.

Abstract

We define a proper moduli stack for degree $p$ covers $f:Y \to \cX$ where $\cX$ is a twisted stable curve in the sense of [5] and [4], and $Y$ is a stable curve which via $f$ is a torsor over $\cX$ under a finite flat group scheme $\cG \to \cX$.