Ramification jump in model extensions of degree $p$

An extension of complete dicrete valuation fields with imperfect residue fields is naturally viewed as an epimorphism between algebraic surfaces with distinguished point. Each regular curve that meets this point with irreducible preimage gives rise to an extension of fields of functions. In this paper a ramification jump of this extension is considered as a function of a jet of a curve. After a topology on a set of jets is introduced, lower semicontinuity and existence of common value for the jump are proved.