Holomorphic differentials of certain solvable covers of the projective line over a perfect field

TL;DR

This paper constructs explicit bases for holomorphic differentials on certain solvable covers of the projective line over fields of positive characteristic, and analyzes their Galois module structure.

Contribution

It introduces a Boseck-type basis for holomorphic differentials on a broad class of solvable covers and describes their Galois module structure for abelian cases.

Findings

Explicit Boseck-type basis for holomorphic differentials

Description of Galois module structure for abelian covers

Applicable to a large class of solvable covers

Abstract

We provide a Boseck-type basis of the space of holomorphic differentials for a large class of solvable covers of the projective line with perfect field of constants of characteristic $p > 0$. Within this class, we also describe the Galois module structure of holomorphic differentials for abelian covers.