On a geometric description of ${\rm Gal}(\overline {\mathbf {Q}}\sb p/\mathbf {Q}\sb {p})$ and a p-adic avatar of $\widehat{GT}$
André, Yves
Duke Math. J., Tome 120 (2003) no. 3, p. 1-39 / Harvested from Project Euclid
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We develop a p-adic version of the so-called Grothendieck-Teichmüller theory (which studies ${\rm Gal}( \mathbf{\bar Q}/\mathbf{Q})$ by means of its action on profinite braid groups or mapping class groups). For every place v of $\overline {\mathbf {Q}}$ , we give some geometrico-combinatorial descriptions of the local Galois group ${\rm Gal}(\overline {\mathbf {Q}}\sb v/\mathbf {Q}\sb v)$ inside ${\text{Gal}}( {{\mathbf{\bar Q}}/{\mathbf{Q}}})$ . We also show that ${\rm Gal}(\overline {\mathbf {Q}}\sb p/\mathbf {Q}\sb {p})$ is the automorphism group of an appropriate $\pi\sb 1$ -functor in p-adic geometry.
Publié le : 2003-07-15
Classification:  11S20,  14G20,  14G32,  20Fxx 
@article{1082744704,
     author = {Andr\'e, Yves},
     title = {On a geometric description of ${\rm Gal}(\overline {\mathbf {Q}}\sb p/\mathbf {Q}\sb {p})$ 
 and a p-adic avatar of $\widehat{GT}$},
     journal = {Duke Math. J.},
     volume = {120},
     number = {3},
     year = {2003},
     pages = { 1-39},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082744704}
}

André, Yves. On a geometric description of ${\rm Gal}(\overline {\mathbf {Q}}\sb p/\mathbf {Q}\sb {p})$ 
 and a p-adic avatar of $\widehat{GT}$. Duke Math. J., Tome 120 (2003) no. 3, pp.  1-39. http://gdmltest.u-ga.fr/item/1082744704/