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 $(\delta_i,\omega_i)$, where $\delta_i$ is a positive rational number and $\omega_i$ 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 $K$.