Overview
- First textbook offering a complete exposition of local and global class field theory as well as arithmetic duality theorems
- Provides the necessary background in Galois cohomology and homological algebra
- Includes an appendix on analytical methods
Part of the book series: Universitext (UTX)
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Table of contents (18 chapters)
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Front Matter
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Group Cohomology and Galois Cohomology: Generalities
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Front Matter
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Duality Theorems
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Front Matter
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Keywords
About this book
Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem.
Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.
Reviews
“For students with no prior understanding of class field theory, the book is ideal. It is self-contained, and is based on a concatenation of master’s level courses given by the author. … his book seamlessly stitches together all the components in a neat and lucid manner. The whole process of learning this classical theory from Harari’s book makes it a painless and enjoyable experience. … The author takes a lot of care to make illuminating remarks in each chapter …” (Balasubramanian Sury, zbMATH 1466.11086, 2021)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Galois Cohomology and Class Field Theory
Authors: David Harari
Translated by: Andrei Yafaev
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-030-43901-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-43900-2Published: 24 June 2020
eBook ISBN: 978-3-030-43901-9Published: 24 June 2020
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIV, 338
Number of Illustrations: 48 b/w illustrations, 2 illustrations in colour
Additional Information: English translation of the original French edition published by EDP Sciences, Les Ulis, 2017. Jointly published with EDP Sciences, Les Ulis, France
Topics: Number Theory