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Wintenberger’s functor for abelian extensions

Kevin Keating — 2009

Journal de Théorie des Nombres de Bordeaux

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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