Galois extensions, plus closure, and maps on local cohomology
Akiyoshi Sannai, Anurag K. Singh

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 of prime characteristic that is a homomorphic image of a Gorenstein ring, Huneke and Lyubeznik proved that there exists a module-finite extension domain such that the induced map on local cohomology modules is zero for each . We prove that the extension may be chosen to be generically Galois, and analyze the Galois groups that arise.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory
