English

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 pp 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 pp-torsion of the Galois group is annihilated by pp.

Keywords

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

R2 v1 2026-06-28T15:13:02.876Z