Hardcover ISBN:  9780821844267 
Product Code:  CHEL/366.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470415747 
Product Code:  CHEL/366.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Hardcover ISBN:  9780821844267 
eBook: ISBN:  9781470415747 
Product Code:  CHEL/366.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $114.10 $91.35 
Hardcover ISBN:  9780821844267 
Product Code:  CHEL/366.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470415747 
Product Code:  CHEL/366.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Hardcover ISBN:  9780821844267 
eBook ISBN:  9781470415747 
Product Code:  CHEL/366.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $114.10 $91.35 

Book DetailsAMS Chelsea PublishingVolume: 366; 2008; 192 ppMSC: Primary 11;
This classic book, originally published in 1968, is based on notes of a yearlong 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.
ReadershipGraduate students and research mathematicians interested in number theory.

Table of Contents

Chapters

Preliminaries

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


Additional Material

Reviews

This new edition of the famous ArtinTate notes on class field theory is a musthave, 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


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This classic book, originally published in 1968, is based on notes of a yearlong 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.

Chapters

Preliminaries

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

This new edition of the famous ArtinTate notes on class field theory is a musthave, 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