  We develop a new approach to construction of numerical invariants for
ramified coverings of algebraic surfaces of prime characteristic.
  Let A be a two-dimensional regular local ring of prime characteristic p with
algebraically closed residue field. Let L/K be a solvable finite Galois
extension of its fraction field. Let C be a germ of a regular curve on the
spectrum of A which is not a component of the ramification divisor R. Then L/K
determines (up to conjugation) an extension of the function filed of C. This is
an extension of discrete valuation fields with algebaically closed residue
fields, and we consider ramification jumps of this extension. Varying C, we
obtain a collection of data describing the ramification of L/K with respect to
C.
  In the present paper we show that the above mentioned ramification jumps
depend only on the jet of C of certain order, and the upper bound for this
order depends linearly on the order of tangence of C and R. Strictly speaking,
this is done for wild ramification jumps, i.e., for the ramification jumps
divided by the order of tame ramification.
  It would be important to prove a stronger fact: not only the jumps but the
whole ramification filtration is the same when C is running over a jet of
certain order. This statement (for curves transversal to R) is a step in
Deligne's program describing how to compute Euler-Poincare characteristics of
constructible etale sheaves on surfaces. In the present version we prove the
above fact for some class of Galois groups that includes, in particular, all
abelian p-groups.
