On the existence of a torsor structure for Galois covers over a complete discrete valuation ring

TL;DR

This paper explores whether Galois covers over complete discrete valuation rings with abelian Galois groups of type (p,p,...,p) can be structured as torsors, addressing a fundamental question in algebraic geometry.

Contribution

It investigates the existence of torsor structures for specific Galois covers over complete discrete valuation rings with abelian Galois groups of type (p,p,...,p).

Findings

Provides conditions for the existence of torsor structures.

Identifies cases where torsor structures do or do not exist.

Contributes to understanding Galois covers in positive residue characteristic.

Abstract

In this note we investigate the problem of existence of a torsor structure for Galois covers of (formal) schemes over a complete discrete valuation ring of residue characteristic $p>0$ in the case of abelian Galois groups of type (p,p,...,p).