β Scribed by Nancy Childress (auth.)
No coin nor oath required. For personal study only.
Class field theory, the study of abelian extensions of algebraic number fields, is one of the largest branches of algebraic number theory. It brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. Some of its consequences (e.g., the Chebotarev density theorem) apply even to nonabelian extensions.
This book is an accessible introduction to class field theory. It takes a traditional approach in that it presents the global material first, using some of the original techniques of proof, but in a fashion that is cleaner and more streamlined than most other books on this topic.
It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included exercises throughout the text.
Professor Nancy Childress is a member of the Mathematics Faculty at Arizona State University.
Number Theory
π SIMILAR VOLUMES
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 spectac
These12 are the notes for Math 776, University of Michigan, Winter 1997, slightly revised from those handed out during the course. They have been substantially revised and expanded from an earlier version, based on my notes from 1993 (v2.01).My approach to class field theory in these notes is eclect