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Field name	Details
Dewey Class	512
Title	The Absolute Galois Group of a Semi-Local Field ([EBook] /) / by Dan Haran, Moshe Jarden.
Author	Haran, Dan
Added Personal Name	Jarden, Moshe
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2021.
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2021.
Physical Details	XVI, 137 p. : online resource.
Series	Springer monographs in mathematics 2196-9922
ISBN	9783030891916
Summary Note	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.:
Contents note	- 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.
Mode of acces to digital resource	Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-89191-6
Links to Related Works	Subject References: Algebra . Algebraic fields . Algebraic Geometry . Field Theory and Polynomials . Polynomials . Authors: author . Haran, Dan . Jarden, Moshe . Corporate Authors: SpringerLink (Online service) . Series: Springer monographs in mathematics . Classification: 512 .

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The Absolute Galois Group of a Semi-Local Field

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