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On a geometric description of $Gal(\bar{\bf Q}_p/{\bf Q}_p)$ and a p-adic avatar of $\hat{GT}$

Yves André
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Abstract

We develop a $p$-adic version of the so-called Grothendieck-Teichmüller theory (which studies $Gal(\bar{\bf Q}/{\bf Q})$ by means of its action on profinite braid groups or mapping class groups). For every place $v$ of $\bar{\bf Q}$, we give some geometrico-combinatorial descriptions of the local Galois group $Gal(\bar{\bf Q}_v/{\bf Q}_v)$ inside $Gal(\bar{\bf Q}/{\bf Q})$. We also show that $Gal(\bar{\bf Q}_p/{\bf Q}_p)$ is the automorphism group of an appropriate $π_1$-functor in $p$-adic geometry.

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Yves André. 2002-10-24. On a geometric description of $Gal(\bar{\bf Q}_p/{\bf Q}_p)$ and a p-adic avatar of $\hat{GT}$. https://arxiv.org/abs/math/0203181

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