Deformation of Curves with Automorphisms and representations on   Riemann-Roch spaces
  We study the deformation theory of nonsigular projective curves defined over algebraic closed fields of positive characteristic. We show that under some assumptions the local deformation problem for automorphisms of powerseries can be reduced to a deformation problem for matrix representations. We study both equicharacteristic and mixed deformations in the case of two dimensional representations. 
Aristides Kontogeorgis