Fiercely ramified cyclic extensions of p-adic fields with imperfect residue field

Abstract

We study the ramification of fierce cyclic Galois extensions of a local field K of characteristic zero with a one-dimensional residue field of characteristic p > 0. Using Kato’s theory of the refined Swan conductor, we associate to such an extension a ramification datum, consisting of a sequence of pairs (δ i , ω i ), where δ i is a positive rational number and ω i a differential form on the residue field of K. Our main result gives necessary and sufficient conditions on such sequences to occur as a ramification datum of a fierce cyclic extension of K.