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 $K$.

arXiv comment27 pages, revised version. Among other things, the referee has pointed out that Lemma 7.1 was incorrect. This has been corrected in the new version

References in corpus (1)

• Wild cyclic-by-tame extensions