Wintenberger's Functor for Abelian Extensions

2008/05/19 by Kevin Keating, Keating, Kevin
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Pharmacological Effects of Natural Compounds #math.NT #msc:11S15

paper · pdf · doi:10.48550/arxiv.0805.2932

12 pages

arxiv created 2008/05/19 · arxiv updated 2009/12/01

Abstract

Let k be a finite field. Wintenberger used the field of norms to give an equivalence between a category whose objects are totally ramified abelian p-adic Lie extensions E/F, where F is a local field with residue field k, and a category whose objects are pairs (K,A), where K≅ k((T)) and A is an abelian p-adic Lie subgroup of \Aut_k(K). In this paper we extend this equivalence to allow \Gal(E/F) and A to be arbitrary abelian pro-p groups.

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