The Hurwitz tree obstruction for the refined local lifting problem

TL;DR

This paper introduces differential Hurwitz tree obstructions to analyze the refined local lifting problem, focusing on conditions for their vanishing in cyclic covers, and sets the stage for future solutions.

Contribution

It formulates differential Hurwitz tree obstructions for the refined local lifting problem and examines their vanishing in cyclic covers, advancing the theoretical framework.

Findings

Obstructions formulated for the refined local lifting problem

Conditions identified for vanishing of obstructions in cyclic covers

Framework set for future solutions to the lifting problem

Abstract

In this manuscript, we formulate the differential Hurwitz tree obstructions for the refined local lifting problem. We specifically explore the circumstances under which these obstructions vanish for cyclic covers. The constructions presented in this paper will be used to address the refined local lifting problem in our forthcoming works.