Valuation rings of dimension one as limits of smooth algebras

2020/06/16 by Dorin Popescu, Popescu, Dorin
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2006.08972

openalex publication_date 2020/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As in Zariski's Uniformization Theorem we show that a valuation ring V of characteristic p>0 of dimension one is a filtered direct limit of smooth \bf F_p-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.

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