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

2011/04/19 by Stefan Wewers, Wewers, Stefan
Mathematics · #11S15 #11S31 #14F05 #19F05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories #math.AG #math.NT #msc:11S15 #msc:11S31 #msc:14F05 #msc:19F05

paper · pdf · doi:10.48550/arxiv.1104.3785

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

openalex publication_date 2011/04/19 · arxiv created 2012/12/09 · arxiv updated 2012/12/11 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

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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