Relevements des revetements de courbes faiblement ramifies (Lifts of weakly ramified coverings of curves)

Let X be a smooth projective curve over a field of characteristic p>0 and G a finite group of automorphism of X. Let n(X,G) be the characteristic of the versal equivariant deformation ring R(X,G) of (X,G). When the ramification is weak (i.e. all second ramification groups are trivial),we prove that n(X,G) is 0 or p and we compute R(X,G).