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Class Field Theory

Publisher: 
American Mathematical Society
Number of Pages: 
192
Price: 
35.00
ISBN: 
9780821844267

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. It's fairly easy to explain why. For one thing, this is a classic, a book that has inspired a generation of number theorists. It has long been out of print and hard to get, however.

But the big news is that the new edition has been entirely re-set using TeX. Tate has taken advantage of this to update and correct the notes, adding footnotes, references, and two new mathematical sections: one sketching the analytic proof of the “second inequality” and another on Weil groups. This has, of course, made a very good book even better.

Most of us, I think, would not want to start our study of class field theory with this book, but aspiring number theorists will want to get to it at some point. It's hard going but deep, insightful, and essential.


Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.


Date Received: 
Tuesday, December 30, 2008
Reviewable: 
Yes
Include In BLL Rating: 
Yes
Emil Artin and John Tate
Series: 
AMS/Chelsea Publishing 366
Publication Date: 
2009
Format: 
Paperback
Category: 
Monograph
Fernando Q. Gouvêa
04/2/2009
BLL Rating: 

 

  • 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
Publish Book: 
Modify Date: 
Sunday, May 31, 2009

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