Given a complex surface and an automorphism of prime order p, the singularities of the quotient of the surface by the action of the automorphism are well understood, and are resolved by a chain of rational curves. On the other hand, very few results are known on the quotient singularities in the analoguous situation in mixed or equicharacteristic p. I will discuss some general facts concerning the resolution graphs of such singularities, with special emphasis on the singularities obtained when constructing models of curves.