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In this article we prove a local Riemman-Hurwitz formula which compares thedimensions 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 theformula proven by the first author in the case of Galois covers of degree p. Wealso investigate the problem of the existence of a torsor structure for afinite Galois cover of type (p,p,...,p) between p-adic schemes.

Galois covers of type (p,...,p), vanishing cycles formula, and the existence of torsor structures