On Abelian extensions in mixed characteristic and ramification in codimension one
Commutative Algebra
2025-05-21 v2 Algebraic Geometry
Abstract
A theorem of Paul Roberts states that the integral closure of a regular local ring in a generically abelian extension is Cohen-Macaulay, provided the characteristic of the residue field does not divide the order of the Galois group. An example of Koh shows the conclusion is false in the modular case. After a modification to the statement concerning ramification over in codimension one, we give an extension of Roberts's theorem to the modular case for unramified regular local rings in mixed characteristic when the -torsion of the Galois group is annihilated by .
Cite
@article{arxiv.2403.04972,
title = {On Abelian extensions in mixed characteristic and ramification in codimension one},
author = {Daniel Katz and Prashanth Sridhar},
journal= {arXiv preprint arXiv:2403.04972},
year = {2025}
}
Comments
Minor revsion. Final version to appear in Int. Math. Res. Not