Multivariate Hensel Lemma for ultrametric fields
Commutative Algebra
2024-02-22 v3
Abstract
The Multivariate Hensel Lemma for local rings is usually proved as a consequence of the Grothendieck version of Zariski's Main Theorem. This version deals with a more general situation that is a priori much more difficult. In this paper, we give a direct proof of the Multivariate Hensel Lemma for ultrametric fields, in the framework of constructive mathematics and without using~ZMT. In the framework of classical mathematics, our result entails the Lemma for rank-one valued fields.
Keywords
Cite
@article{arxiv.2301.06546,
title = {Multivariate Hensel Lemma for ultrametric fields},
author = {M. -E. Alonso and H. Lombardi and S. Neuwirth},
journal= {arXiv preprint arXiv:2301.06546},
year = {2024}
}
Comments
In this file you find the English version, 15 pages, starting on the page numbered E1. Then the French version (Lemme de Hensel multivari\'e pour les corps ultram\'etriques), 15 pages, begins on the page numbered F1