Class Field Theory
About this Title
Emil Artin and John Tate, University of Texas at Austin, Austin, TX
Publication: AMS Chelsea Publishing
Publication Year: 2008; Volume 366
ISBNs: 978-0-8218-4426-7 (print); 978-1-4704-1574-7 (online)
This classic book, originally published in 1968, is based on notes of a year-long seminar the authors ran at Princeton University. The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory, and the authors accomplished this goal spectacularly: for more than 40 years since its first publication, the book has served as an ultimate source for many generations of mathematicians.
In this revised edition, two mathematical additions complementing the exposition in the original text are made. The new edition also contains several new footnotes, additional references, and historical comments.
Graduate students and research mathematicians interested in number theory.
Table of Contents
- Chapter V. The first fundamental inequality
- Chapter VI. Second fundamental inequality
- Chapter VII. Reciprocity law
- Chapter VIII. The existence theorem
- Chapter IX. Connected component of idèle classes
- Chapter X. The Grunwald–Wang theorem
- Chapter XI. Higher ramification theory
- Chapter XII. Explicit reciprocity laws
- Chapter XIII. Group extensions
- Chapter XIV. Abstract class field theory
- Chapter XV. Weil groups