THE ABSOLUTE GALOIS GROUP OF SUBFIELDS OF THE FIELD OF TOTALLY S-ADIC NUMBERS

被引：3

作者：

Haran, Dan ^{[1
]}

Jarden, Moshe ^{[1
]}

Pop, Florian ^{[2
]}

机构：

[1] Tel Aviv Univ, Sch Math, IL-69978 Tel Aviv, Israel

[2] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

来源：

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI | 2012年 / 46卷 / 02期

基金：

美国国家科学基金会;

关键词：

Hilbertian field; local primes; totally S-adic numbers; Haar measure; absolute Galois group; free product;

D O I：

10.7169/facm/2012.46.2.6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a finite set S of local primes of a countable Hilbertian field K and for sigma(1),...,sigma(e) is an element of Gal(K) we denote the field of totally S-adic numbers by K-tot,(S), the fixed field of sigma(1),...,sigma(e) in K-tot,(S) by K-tot,K-S (sigma), and the maximal Galois extension of K in K-tot,K-S(sigma) by K-tot,K-S [sigma]. We prove that for almost all sigma is an element of Gal(K)(e) the absolute Galois group of K-tot,K-S [sigma] is isomorphic to the free product of (F) over cap (omega) and a free product of local factors over S.

引用

页码：205 / 223

页数：19

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