Overview
- Traditional approach, but cleaner and more streamlined than most others
- Accessible introduction to class field theory
- Lots of challenging exercises
Part of the book series: Universitext (UTX)
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Table of contents (7 chapters)
Keywords
About this book
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 attempts to present the material using the original techniques of proof (global to local), but in a fashion which 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.
Reviews
From the reviews:
"This book has grown out of lectures on the subject by the author. … it must have been fun for both the author presenting these courses on class field theory and the students taking them and eager to learn the subject. … list of contents may give a good impression of how class field theory is developed in this book. … each chapter is commenced by a short introduction describing what is going on next. I enjoyed seeing explicit examples and nice applications … ." (Jürgen Ritter, Mathematical Reviews, Issue 2009 i)
"Class field theory studies abelian extensions of number fields and their completions. … The clarity of the exposition and the many exercises ranging from routine to quite challenging problems make the book perfect for a first introduction to class field theory." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1165, 2009)
“In a fast ride, running half the length of many competing volumes, Childress (Arizona State) employs a balanced mix of standard tools for a remarkably honed introduction … . Good to read alongside fleshier accounts; probably more accessible … . Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 47 (3), November, 2009)
“This is a first introduction to class field theory. … The author succeeds in making the material accessible by proceeding at a moderate pace. This relatively slim book is a good choice for anyone who wants to get an idea of what class field theory is about before tackling a more comprehensive textbook or monograph.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 164 (3), November, 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Class Field Theory
Authors: Nancy Childress
Series Title: Universitext
DOI: https://doi.org/10.1007/978-0-387-72490-4
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2009
Softcover ISBN: 978-0-387-72489-8Published: 24 November 2008
eBook ISBN: 978-0-387-72490-4Published: 28 October 2008
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: X, 226