國立高雄大學圖資館 |

Language: English

Back

The absolute Galois group of a semi-...

Haran, Dan.

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 fieldby 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$q(electronic bk.)

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$q(electronic bk.)

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

190982
Galois theory.

LC Class. No.: QA214 / .H37 2021

Dewey Class. No.: 512.32

The absolute Galois group of a semi-local field
LDR:02063nmm 22003255a 4500 001 614071
003 DE-He213
005 20211119130656.0
006 m d
007 cr nn 008maaau
008 220627s2021 sz s 0 eng d
020 $a 9783030891916$q(electronic bk.)
020 $a 9783030891909$q(paper)
024 7 $a 10.1007/978-3-030-89191-6 $2 doi
035 $a 978-3-030-89191-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA214 $b .H37 2021
072 7 $a PBF $2 bicssc
072 7 $a MAT002000 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.32 $2 23
090 $a QA214 $b .H254 2021
100 1 $a Haran, Dan. $3 912218
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.
650 0 $a Galois theory. $3 190982
650 1 4 $a Algebra. $3 188312
650 2 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Field Theory and Polynomials. $3 274058
700 1 $a Jarden, Moshe. $3 256421
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 557774
856 4 0 $u https://doi.org/10.1007/978-3-030-89191-6
950 $a Mathematics and Statistics (SpringerNature-11649)