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

共 39 条

[21] GROUP AUTOMORPHISMS OF ABSOLUTE GALOIS GROUP OF RATIONAL NUMBER-FIELD
IKEDA, M
ARCHIV DER MATHEMATIK, 1975, 26 (03) : 250 - 252
[22] COMPLETENESS OF ABSOLUTE GALOIS GROUP OF RATIONAL NUMBER-FIELD
IKEDA, M
ARCHIV DER MATHEMATIK, 1975, 26 (06) : 602 - 605
[23] THE ABSOLUTE GALOIS GROUP OF A PSEUDO REAL CLOSED ALGEBRAIC FIELD
HARAN, D
JARDEN, M
PACIFIC JOURNAL OF MATHEMATICS, 1986, 123 (01) : 55 - 69
[24] COMPLETENESS OF ABSOLUTE GALOIS GROUP OF RATIONAL NUMBER-FIELD
IKEDA, M
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1977, 291 : 1 - 22
[25] Explicit uniformizers for certain totally ramified extensions of the field of p-adic numbers
Hugues Bellemare
Antonio Lei
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2020, 90 : 73 - 83
[26] Explicit uniformizers for certain totally ramified extensions of the field of p-adic numbers
Bellemare, Hugues
Lei, Antonio
ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2020, 90 (01): : 73 - 83
[27] Singular probability distributions and fractal properties of sets of real numbers defined by the asymptotic frequencies of their s-adic digits
Albeverio S.
Prats'Ovytyi M.
Torbin G.
Ukrainian Mathematical Journal, 2005, 57 (9) : 1361 - 1370
[28] The absolute Galois group of a p-adic fieldIn Erinnerung an Jürgen Ritter (1943–2021)
Moshe Jarden
Mark Shusterman
Mathematische Annalen, 2023, 386 : 1595 - 1603
[29] THE ABSOLUTE GALOIS GROUP OF A PSEUDO P-ADICALLY CLOSED FIELD
HARAN, D
JARDEN, M
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1988, 383 : 147 - 206
[30] On Geary's theorem for the field of p-adic numbers
Myronyuk, M. V.
Feldman, G. M.
DOKLADY MATHEMATICS, 2016, 93 (02) : 152 - 154

← 1 2 3 4 →