  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.
