Wintenberger’s functor for abelian extensions

Keating, Kevin. "Wintenberger’s functor for abelian extensions." Journal de Théorie des Nombres de Bordeaux 21.3 (2009): 665-678. <http://eudml.org/doc/10903>.

@article{Keating2009,
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 $K\cong k((T))$ and $A$ is an abelian $p$-adic Lie subgroup of $\mathrm\{Aut\}_k(K)$. In this paper we extend this equivalence to allow $\mathrm\{Gal\}(E/F)$ and $A$ to be arbitrary abelian pro-$p$ groups.},
affiliation = {Department of Mathematics University of Florida Gainesville, FL 32611 USA},
author = {Keating, Kevin},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {ramification; field of norms; extensions of local fields; automorphisms of local fields.},
language = {eng},
number = {3},
pages = {665-678},
publisher = {Université Bordeaux 1},
title = {Wintenberger’s functor for abelian extensions},
url = {http://eudml.org/doc/10903},
volume = {21},
year = {2009},
}

TY - JOUR
AU - Keating, Kevin
TI - Wintenberger’s functor for abelian extensions
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2009
PB - Université Bordeaux 1
VL - 21
IS - 3
SP - 665
EP - 678
AB - 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 $\mathrm{Aut}_k(K)$. In this paper we extend this equivalence to allow $\mathrm{Gal}(E/F)$ and $A$ to be arbitrary abelian pro-$p$ groups.
LA - eng
KW - ramification; field of norms; extensions of local fields; automorphisms of local fields.
UR - http://eudml.org/doc/10903
ER -