  We study $p$-group Galois covers $X \rightarrow \mathbb{P}^1$ with only one
fully ramified point. These covers are important because of the Katz-Gabber
compactification of Galois actions on complete local rings. The sequence of
ramification jumps is related to the Weierstrass semigroup of the global cover
at the stabilized point. We determine explicitly the jumps of the ramification
filtrations in terms of pole numbers. We give applications for curves with zero
$p$--rank: we focus on maximal curves and curves that admit a big action.
  Moreover the Galois module structure of polydifferentials is studied and an
application to the tangent space of the deformation functor of curves with
automorphisms is given.
