The Absolute Galois Group of a Semi-Local Field
Series: Springer Monographs in Mathematics;
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Product details:
- Edition number 1st ed. 2021
- Publisher Springer
- Date of Publication 21 November 2022
- Number of Volumes 1 pieces, Book
- ISBN 9783030891930
- Binding Paperback
- No. of pages137 pages
- Size 235x155 mm
- Weight 250 g
- Language English
- Illustrations XVI, 137 p. 456
Categories
Short description:
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 fieldarithmetic, Galois theory and profinite groups.
MoreLong description:
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.
More
Table of Contents:
- 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.
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