Topics in higher ramification theory I
Commutative Algebra
2026-05-04 v3
Abstract
We introduce and study the notion of ramification ideals in higher ramification theory. After general results on their computation, we discuss their connection with defect and compute them for Artin-Schreier extensions and Kummer extensions of prime degree equal to the residue characteristic, with or without defect. We present an example that shows that nontrivial defect in an extension of degree not a prime may not imply the existence of a nonprincipal ramification ideal.
Keywords
Cite
@article{arxiv.2503.13157,
title = {Topics in higher ramification theory I},
author = {Franz-Viktor Kuhlmann},
journal= {arXiv preprint arXiv:2503.13157},
year = {2026}
}
Comments
This is the much extended first half of the previous version. The second half will be used as the basis for another paper with title "Topics in higher ramification theory II"