On ramification in transcendental extensions of local fields

Abstract

Let L/K be an extension of complete discrete valuation fields, and assume that the residue field of K is perfect and of positive characteristic. The residue field of L is not assumed to be perfect.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.