Uniformisation locale des schémas quasi-excellents de caractéristique nulle

2013/11/14 by Jean-Christophe San Saturnino, Saturnino, Jean-Christophe San · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1311.3525

openalex publication_date 2013/11/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove an embedded local uniformization theroem for a valuation centered on a point of a quasi-excellent scheme of characteristic zero. The proof reduces to valuations of rank 1 and consists in desingularizing the ideal formed by the elements of infinite value and monomializing the key polynomials. We then prove a monomialization theorem valid in all characteristic under certain conditions, including that of non-existence of limit key polynomials, a condition that is always satified in characteristic zero.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

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• Defect of an extension, key polynomials and local uniformization

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