The absolute galois group of subfields of the field of totally S-ADIC numbers

Dan Haran; Moshe Jarden; Florian Pop

doi:10.7169/facm/2012.46.2.6

The absolute galois group of subfields of the field of totally S-ADIC numbers

Dan Haran, Moshe Jarden, Florian Pop

School of Mathematical Sciences

University of Pennsylvania

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

For a finite set S of local primes of a countable Hilbertian field K and for δ1; δe 2 Gal(K) we denote the field of totally S-Adic numbers by Ktot;S, the fixed field of δ1; δe in Ktot;S by Ktot;S(δ), and the maximal Galois extension of K in Ktot;S(δ) by Ktot;S[δ]. We prove that for almost all δ € Gal(K)e the absolute Galois group of Ktot;S[δ] is isomorphic to the free product of Fω and a free product of local factors over S.

Original language	English
Pages (from-to)	205-223
Number of pages	19
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	46
Issue number	2
DOIs	https://doi.org/10.7169/facm/2012.46.2.6
State	Published - 2012

Keywords

Absolute Galois Group
Free Product
Haar measure
Hilbertian field
Local Primes
Totally S-Adic numbers

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10.7169/facm/2012.46.2.6

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abstract = "For a finite set S of local primes of a countable Hilbertian field K and for δ1; δe 2 Gal(K) we denote the field of totally S-Adic numbers by Ktot;S, the fixed field of δ1; δe in Ktot;S by Ktot;S(δ), and the maximal Galois extension of K in Ktot;S(δ) by Ktot;S[δ]. We prove that for almost all δ € Gal(K)e the absolute Galois group of Ktot;S[δ] is isomorphic to the free product of Fω and a free product of local factors over S.",

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AB - For a finite set S of local primes of a countable Hilbertian field K and for δ1; δe 2 Gal(K) we denote the field of totally S-Adic numbers by Ktot;S, the fixed field of δ1; δe in Ktot;S by Ktot;S(δ), and the maximal Galois extension of K in Ktot;S(δ) by Ktot;S[δ]. We prove that for almost all δ € Gal(K)e the absolute Galois group of Ktot;S[δ] is isomorphic to the free product of Fω and a free product of local factors over S.

KW - Absolute Galois Group

KW - Free Product

KW - Haar measure

KW - Hilbertian field

KW - Local Primes

KW - Totally S-Adic numbers

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The absolute galois group of subfields of the field of totally S-ADIC numbers

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