Keating: Wintenberger’s functor for abelian extensions

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Kevin Keating
Wintenberger’s functor for abelian extensions
Journal de théorie des nombres de Bordeaux, 21 no. 3 (2009), p. 665-678
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Résumé - 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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