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The Absolute Galois Group of the Field of Totally S-Adic Numbers

Published online by Cambridge University Press:  11 January 2016

Dan Haran ,
Moshe Jarden  and
Florian Pop
Dan Haran
Affiliation:
School of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel, haran@post.tau.ac.il
Moshe Jarden
Affiliation:
School of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel, jarden@post.tau.ac.il
Florian Pop
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, USA, pop@math.upenn.edu
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Abstract

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For a finite set S of primes of a number field K and for σ1,…, σe ∈ Gal(K) we denote the field of totally S-adic numbers by Ktot,S and the fixed field of σ1,…,σe in Ktot,S by Ktot,S(σ). We prove that foralmost all σ ∈ Gal(K)e the absolute Galois group of Ktot,S(σ) is the free product of and a free product of local factors over S.

Keywords

12E30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 194 , 2009 , pp. 91 - 147
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

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