Equidistant liftings of elementary abelian Galois covers of curves

In this paper, we discuss the local lifting problem for the action of elementary abelian groups. Studying logarithmic differential forms linked to deformations of \((\mu_p)^n\)-torsors, we show necessary conditions on the set of ramification points in order to get equidistant liftings. Such conditions of combinatoric nature lead us to show new obstructions to lifting actions of Z/3Z x Z/3Z.