Grinberg-Kazhdan theorem and Newton groupoids

2018/01/03 by Vladimir Drinfeld, Drinfeld, Vladimir · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1801.01046

openalex publication_date 2018/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first prove the Grinberg-Kazhdan formal arc theorem without any assumptions on the characteristic. This part of the article is equivalent to arXiv:math-AG/0203263. Then we try to clarify the geometric ideas behind the proof by introducing the notion of Newton groupoid (which is related to Newton's method for finding roots). Newton groupoids are certain groupoids in the category of schemes associated to any generically etale morphism from a locally complete intersection to a smooth variety.

Citations

• Lectures on Integrability of Lie Brackets
• On the Grinberg - Kazhdan formal arc theorem

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