Universitext

Galois Cohomology and Class Field Theory

Authors: Harari, David

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  • 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
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eBook $44.99
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  • ISBN 978-3-030-43901-9
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Softcover $59.99
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About this Textbook

This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory.

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.

About the authors

David Harari is a professor at the Université Paris-Sud (Orsay). He is a specialist in arithmetic and algebraic geometry, author of 40 research papers in these fields.

Table of contents (18 chapters)

Table of contents (18 chapters)

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-030-43901-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
  • Institutional customers should get in touch with their account manager
Softcover $59.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Galois Cohomology and Class Field Theory
Authors
Translated by
Yafaev, A.
Series Title
Universitext
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-43901-9
DOI
10.1007/978-3-030-43901-9
Softcover ISBN
978-3-030-43900-2
Series ISSN
0172-5939
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
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