On ramification in transcendental extensions of local fields

In this paper, we prove a formula for the Swan conductor of the image of a character χ∈H1(K,Q/Z) in H1(L,Q/Z) for χ sufficiently ramified. Further, we define generalizations ψL/Kab and ψL/KAS of the classical ψ-function and prove a formula for ψL/Kab(t) for sufficiently large t∈R.