Wintenberger's Functor for Abelian Extensions

Details Wintenberger's Functor for Abelian Extensions Wintenberger's Functor for Abelian Extensions

2008-05-19

arxiv.org/abs/0805.2932v1

Mathematics

Number Theory

12 pages

Scientific paper

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 $K\cong k((T))$ 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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