# A cohomological treatise of HKG-covers with applications to the Nottingham group

## TL;DR

This paper characterizes HKG-curves using cohomology classes and applies this framework to describe finite subgroups of the Nottingham group, advancing understanding in algebraic geometry and group theory.

## Contribution

It introduces a cohomological approach to characterize HKG-curves and applies it to analyze finite subgroups of the Nottingham group, providing new insights.

## Key findings

- Cohomological characterization of HKG-curves
- Description of finite subgroups of the Nottingham group
- New methods linking algebraic geometry and group theory

## Abstract

We characterize Harbater-Katz-Gabber curves in terms of a family of cohomology classes satisfying a compatibility condition. Our construction is applied to the description of finite subgroups of the Nottingham Group.