On the Krull Dimension of the deformation ring of curves with   automorphisms
  We reduce the study of the Krull dimension d of the deformation ring of the functor of deformations of curves with automorphisms to the study of the tangent space of the deformation functor of a class of matrix representations of the p-part of the decomposition groups at wild ramified points, and we give a method in order to compute d. 
A. Kontogeorgis