Defect of an extension, key polynomials and local uniformization

2014/12/24 by Jean-Christophe San Saturnino, Saturnino, Jean-Christophe San · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1412.7697

openalex publication_date 2014/12/24 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

For all simple and finite extension of a valued field, we prove that its defect is the product of the effective degrees of the complete set of key polynomials associated. As a consequence, we obtain a local uniformization theorem for valuations of rank 1 centered on an equicharacteristic quasi-excellent local domain satisfying some inductive assumptions of lack of defect.

Citations

• Uniformisation locale des schémas quasi-excellents de caractéristique nulle

Cited by

• On Kaplansky's Embedding Theorem

Related

• A characterization for the defect of rank one valued field extensions
• On local uniformization in arbitrary characteristic, I
• On defect in finite extensions of valued fields
• Uniformisation locale des schémas quasi-excellents de caractéristique nulle
• The defect formula