Valuation rings of dimension one as limits of smooth algebras
Commutative Algebra
2025-02-27 v5 Algebraic Geometry
Abstract
As in Zariski's Uniformization Theorem we show that a valuation ring of characteristic of dimension one is a filtered direct limit of smooth -algebras under some conditions of transcendence degree. Under mild conditions, the algebraic immediate extensions of valuation rings are dense if they are filtered direct limit of smooth morphisms.
Keywords
Cite
@article{arxiv.2006.08972,
title = {Valuation rings of dimension one as limits of smooth algebras},
author = {Dorin Popescu},
journal= {arXiv preprint arXiv:2006.08972},
year = {2025}
}
Comments
Theorem 19 is easier in a restrictive case. arXiv admin note: text overlap with arXiv:2004.11004