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

Manuscripta Mathematica volume 143, pages 445–472 (2014)Cite this article

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.

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  1. Institut für Reine Mathematik, Universität Ulm, Helmholtzstr. 18, 89081, Ulm, Germany

    Stefan Wewers

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  1. Stefan Wewers
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Correspondence to Stefan Wewers.

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Wewers, S. Fiercely ramified cyclic extensions of p-adic fields with imperfect residue field. manuscripta math. 143, 445–472 (2014). https://doi.org/10.1007/s00229-013-0630-1

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  • DOI: https://doi.org/10.1007/s00229-013-0630-1

Mathematics Subject Classification (2000)

  • 11S15
  • 11S31
  • 14F05
  • 19F05