We develop a p-adic version of the so-called Grothendieck-Teichmüller theory (which studies by means of its action on profinite braid groups or mapping class groups). For every place v of , we give some geometrico-combinatorial descriptions of the local Galois group inside . We also show that is the automorphism group of an appropriate -functor in p-adic geometry.
Yves André. "On a geometric description of and a p-adic avatar of ." Duke Math. J. 119 (1) 1 - 39, 15 July 2003. https://doi.org/10.1215/S0012-7094-03-11911-0