TITLE: DÉFORMATIONS FORMELLES DE REVÊTEMENTS : UN PRINCIPE LOCAL-GLOBAL

JOSÉ BERTIN ARIANE MÉZARD

Abstract. Let C be a generically smooth, locally complete intersection curve defined over an algebraically closed field k of characteristic p ≥ 0. Let G ⊂ Aut_{k}C be a finite group of automorphisms of C. We develop a theory of G-equivariant deformations of the Galois cover C → C/G. We prove that all obstructions to G-equivariant deformations are local: they are localized at singular and widely ramified points. As an application, we discuss the case of G-equivariant deformations of semi-stable curves.