On a geometric description of Gal(\bf Q_p/\bf Q_p) and a p-adic avatar of GT

2002/03/18 by Yves André, André, Yves
Mathematics · #11R32 #14G20 #14G22 #14H30 #20F28 #20F36 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.AG #math.NT #msc:11R32 #msc:14G20 #msc:14G22 #msc:14H30 #msc:20F28 #msc:20F36

paper · pdf · doi:10.48550/arxiv.math/0203181

version to appear in Duke Math. J

openalex publication_date 2002/03/18 · arxiv created 2002/10/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a p-adic version of the so-called Grothendieck-Teichmüller theory (which studies Gal(\bf Q/\bf Q) by means of its action on profinite braid groups or mapping class groups). For every place v of \bf Q, we give some geometrico-combinatorial descriptions of the local Galois group Gal(\bf Q_v/\bf Q_v) inside Gal(\bf Q/\bf Q). We also show that Gal(\bf Q_p/\bf Q_p) is the automorphism group of an appropriate π₁-functor in p-adic geometry.

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