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2009 The absolute Galois group of the field of totally $S$-adic numbers
Dan Haran, Moshe Jarden, Florian Pop
Nagoya Math. J. 194: 91-147 (2009).

Abstract

For a finite set $S$ of primes of a number field $K$ and for $\sigma_{1}, \dots, \sigma_{e} \in \operatorname{Gal}(K)$ we denote the field of totally $S$-adic numbers by $K_{{\rm tot}, S}$ and the fixed field of $\sigma_{1}, \dots, \sigma_{e}$ in $K_{{\rm tot}, S}$ by $K_{{\rm tot}, S}({\boldsymbol\sigma})$. We prove that for almost all ${\boldsymbol\sigma} \in \operatorname{Gal}(K)^{e}$ the absolute Galois group of $K_{{\rm tot}, S}({\boldsymbol\sigma})$ is the free product of ${\hat F}_{e}$ and a free product of local factors over $S$.

Citation

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Dan Haran. Moshe Jarden. Florian Pop. "The absolute Galois group of the field of totally $S$-adic numbers." Nagoya Math. J. 194 91 - 147, 2009.

Information

Published: 2009
First available in Project Euclid: 17 June 2009

zbMATH: 1261.12006
MathSciNet: MR2536528

Subjects:
Primary: 12E30

Rights: Copyright © 2009 Editorial Board, Nagoya Mathematical Journal

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