On the Galois-module structure of polydifferentials of Artin-Schreier-Mumford curves, modular and integral representation theory

TL;DR

This paper investigates the Galois-module structure of polydifferentials on Mumford curves over fields of positive characteristic, providing explicit computations for Artin-Schreier-Mumford curves using harmonic cocycles.

Contribution

It offers a detailed analysis and explicit description of the holomorphic polydifferentials' structure for Artin-Schreier-Mumford curves, advancing understanding in modular and integral representation theory.

Findings

Explicit structure of holomorphic polydifferentials for Artin-Schreier-Mumford curves

Application of harmonic cocycles to Galois-module analysis

Enhanced understanding of polydifferential modules in positive characteristic

Abstract

We study the Galois-module structure of polydifferentials for Mumford curves, defined over a field of positive charactersitic, using the theory of harmonic cocycles. For the case of Artin-Schreier-Mumford curves the structure of holomorphic polydifferentials is explicitly computed.