Volume: 366; 2008; 192 pp; Hardcover
MSC: Primary 11;
Print ISBN: 978-0-8218-4426-7
Product Code: CHEL/366.H
List Price: $41.00
AMS Member Price: $36.90
MAA Member Price: $36.90
Electronic ISBN: 978-1-4704-1574-7
Product Code: CHEL/366.H.E
List Price: $38.00
AMS Member Price: $30.40
MAA Member Price: $34.20
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Supplemental Materials
Class Field Theory
Share this pageEmil Artin; John Tate
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
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.
Readership
Graduate students and research mathematicians interested in number theory.
Reviews & Endorsements
This new edition of the famous Artin-Tate notes on class field theory is a must-have, even for those who already have a copy of the original. This is a classic, a book that has inspired a generation of number theorists. It's hard going but deep, insightful, and essential.
-- MAA Reviews
Table of Contents
Table of Contents
Class Field Theory
- Cover Cover11
- Title page i2
- Contents iii4
- Preface to the new edition v6
- Preface vii8
- Preliminaries 110
- Chapter V. The first fundamental inequality 1120
- Chapter VI. Second fundamental inequality 1928
- Chapter VII. Reciprocity law 3544
- Chapter VIII. The existence theorem 5564
- Chapter IX. Connected component of idèle classes 6574
- Chapter X. The Grunwald–Wang theorem 7382
- Chapter XI. Higher ramification theory 8392
- Chapter XII. Explicit reciprocity laws 109118
- Chapter XIII. Group extensions 127136
- Chapter XIV. Abstract class field theory 143152
- Chapter XV. Weil groups 167176
- Bibliography 191200
- Back Cover Back Cover1201