Prolongement de revêtements galoisiens en géométrie rigide

In the first part of the paper we study finite Galois coverings of rigid annuli: we show that, up to finite extension of the ground field, an etale covering of an annulus can be extended to a finite covering of the closed disk, branched at a finite number of points. The proof has recourse to the cohomology of the profinite fundamental group of these spaces. These results are then applied to the problem of lifting to a complete discrete valuation ring a finite Galois covering of curves over the residue field; cuspidal singularities have to be introduced when the original covering is wildly ramified.