Galois extensions, plus closure, and maps on local cohomology

TL;DR

This paper investigates Galois extensions in the context of local cohomology, showing that certain module-finite extensions can be chosen to be generically Galois and exploring the associated Galois groups.

Contribution

It extends previous results by demonstrating the existence of generically Galois extensions that induce zero maps on local cohomology, and analyzes the Galois groups involved.

Findings

Existence of generically Galois extensions with zero local cohomology maps

Analysis of Galois groups arising from these extensions

Extension properties in prime characteristic local domains

Abstract

Given a local domain $(R,m)$ of prime characteristic that is a homomorphic image of a Gorenstein ring, Huneke and Lyubeznik proved that there exists a module-finite extension domain $S$ such that the induced map on local cohomology modules $H^i_m(R)\to H^i_m(S)$ is zero for each $i<\dim R$. We prove that the extension $S$ may be chosen to be generically Galois, and analyze the Galois groups that arise.