TY - BOOK

T1 - The absolute Galois group of a semi-local field

AU - Haran, Dan

AU - Jarden, Moshe

N1 - Springer eBooks

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85120869635&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-89191-6

DO - 10.1007/978-3-030-89191-6

M3 - ???researchoutput.researchoutputtypes.bookanthology.book???

AN - SCOPUS:85120869635

SN - 9783030891909

T3 - Springer Monographs in Mathematics

BT - The absolute Galois group of a semi-local field

PB - Springer

CY - Cham, Switzerland

ER -