Ramification of surfaces: Artin-Schreier extensions
  Let $A$ be a regular 2-dimensional local ring of characteristic $p>0$, and let $L/K$ be a cyclic extension of degree $p$ of its field of fractions such that the corresponding branch divisor is normal crossing. For each $\gp\in\Spec A$ of height 1 such that $A/\gp$ is regular, consider the ramification jump $h_\gp$ of the extension of the residue field at $\gp$. In this paper the semi-continuity of $h_\gp$ with respect to Zariski topology of suitable jet spaces is proved. The asymptotic of $h_\gp$ with respect to intersection multiplicity of the prime divisor defined by $\gp$ and the branch divisor is also addressed. 
Igor Zhukov