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

Stefan Wewers

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

Number Theory 2012-12-11 v2 Algebraic Geometry

Authors: Stefan Wewers

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 $K$ .

Keywords

p-adic fields cyclic extension fierce ramification refined Swan conductor imperfect residue field differential form Galois extension

Cite

@article{arxiv.1104.3785,
  title  = {Fiercely ramified cyclic extensions of p-adic fields with imperfect residue field},
  author = {Stefan Wewers},
  journal= {arXiv preprint arXiv:1104.3785},
  year   = {2012}
}

Comments

27 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

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

Abstract

Keywords

Cite

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