Ebook: Class Field Theory

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.

Table of Contents

Preliminaries
The first fundamental inequality
Second fundamental inequality
Reciprocity law
The existence theorem
Connected component of idèle classes
The Grunwald-Wang theorem
Higher ramification theory
Explicit reciprocity laws
Group extensions
Abstract class field theory
Weil groups
Bibliography