A special form of Zariski's Uniformization Theorem in positive characteristic

2025/07/09 by Popescu, Dorin
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.06743

Abstract

This is mainly a small exposition on extensions of valuation rings as a filtered union of smooth algebras.

Citations

• Filtered colimits of complete intersection algebras
• Algebraic valuation ring extensions as limits of complete intersection algebras
• Pure transcendental, immediate valuation ring extensions as limits of smooth algebras
• Extensions of valuation rings containing \bf Q as limits of smooth algebras
• Valuation rings are derived splinters

Related

• Valuation rings of dimension one as limits of smooth algebras
• Néron desingularization of extensions of valuation rings with an Appendix by Kęstutis Česnavičius
• Pure transcendental, immediate valuation ring extensions as limits of smooth algebras
• Extensions of valuation rings containing \bf Q as limits of smooth algebras
• Reduction of local uniformization to the case of rank one valuations for rings with zero divisors