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The absolute Galois group of a semi-...

Haran, Dan.

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The absolute Galois group of a semi-local field

Record Type:	Electronic resources : Monograph/item
Title/Author:	The absolute Galois group of a semi-local field/ by Dan Haran, Moshe Jarden.
Author:	Haran, Dan.
other author:	Jarden, Moshe.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xvi, 137 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Galois theory. -
Online resource:	https://doi.org/10.1007/978-3-030-89191-6
ISBN:	9783030891916

The absolute Galois group of a semi-local field
Haran, Dan.

The absolute Galois group of a semi-local field[electronic resource] /by Dan Haran, Moshe Jarden. - Cham :Springer International Publishing :2021. - xvi, 137 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized inverse problem of Galois theory. Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of free products of profinite groups and their subgroups. The book will be of interest to researchers in field arithmetic, Galois theory and profinite groups.

ISBN: 9783030891916

Standard No.: 10.1007/978-3-030-89191-6doiSubjects--Topical Terms:

523821
Galois theory.

LC Class. No.: QA214 / .H37 2021

Dewey Class. No.: 512.32

The absolute Galois group of a semi-local field
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245 1 4 $a The absolute Galois group of a semi-local field $h [electronic resource] / $c by Dan Haran, Moshe Jarden.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xvi, 137 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
520 $a This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized inverse problem of Galois theory. Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of free products of profinite groups and their subgroups. The book will be of interest to researchers in field arithmetic, Galois theory and profinite groups.
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650 2 4 $a Algebraic Geometry. $3 893861
650 2 4 $a Field Theory and Polynomials. $3 891077
700 1 $a Jarden, Moshe. $3 897494
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