Lifting Artin-Schreier covers with maximal wild monodromy

TL;DR

This paper investigates the lifting of certain p-cyclic covers of the projective line over algebraically closed fields with characteristic p, focusing on cases with maximal wild monodromy, and provides positive results for specific covers.

Contribution

It establishes conditions under which p-cyclic covers with maximal wild monodromy can be lifted, especially for covers birational to w^p - w = tR(t).

Findings

Lifting is possible for covers birational to w^p - w = tR(t).

Provides positive answers to the lifting problem under maximal wild monodromy.

Characterizes when such covers can be lifted over DVRs.

Abstract

Let $k$ be an algebraically closed field of characteristic $p > 0$. We consider the problem of lifting $p$-cyclic covers of $\Proj_k$ as $p$-cyclic covers of the projective line over some DVR under the condition that the wild monodromy is maximal. We answer positively the question for covers birational to $w^ p-w=tR(t)$ for some additive polynomial $R(t)$.