Deformations formelles des revetements sauvagement ramifies de courbes algebriques

Abstract

In this paper we study formal moduli for wildly ramified Galois covering. We prove a local-global principle. We then focus on the infinitesimal deformations of the Z/pZ-covers. We explicitly compute a deformation of an automorphism of order p which implies a universal obstruction for p>2. By deforming Artin-Schreier equations we obtain a lower bound on the dimension of the local versal deformation ring. At last, by comparing the global versal deformation ring to the complete local ring in a point of a moduli space, we determine the dimensions of the global and local versal deformation ring.