  In this article we prove a local Riemman-Hurwitz formula which compares the
dimensions of the spaces of vanishing cycles in a finite Galois cover of type
(p,p,...,p) between formal germs of p-adic curves and which generalises the
formula proven by the first author in the case of Galois covers of degree p. We
also investigate the problem of the existence of a torsor structure for a
finite Galois cover of type (p,p,...,p) between p-adic schemes.
