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The Absolute Galois Group of a Semi-Local Field

Record Type:	Language materials, printed : 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.
Description:	XVI, 137 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Algebra. -
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. - 1st ed. 2021. - XVI, 137 p.online resource. - Springer Monographs in Mathematics,2196-9922. - Springer Monographs in Mathematics,.

- Introduction -- 1. Topologies -- 2. Families of Subgroups -- 3. Free Products of Finitely Many Profinite Groups -- 4. Generalized Free Products.-5. Relative Embedding Problems -- 6. Strong Proper Projectivity -- 7. Étale Profinite Subset of Subgr(G) -- 8. Fundamental Result -- 9. Main Result. Bibliography -- Index.

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:

579870
Algebra.

LC Class. No.: QA150-272

Dewey Class. No.: 512

The Absolute Galois Group of a Semi-Local Field
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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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