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Let be a finite field. Wintenberger used the field of norms to give an equivalence between a category whose objects are totally ramified abelian -adic Lie extensions , where is a local field with residue field , and a category whose objects are pairs , where and is an abelian -adic Lie subgroup of . In this paper we extend this equivalence to allow and to be arbitrary abelian pro- groups.
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