Class Field Theory
Seiten
2008
|
1st Edition.
2nd Printing. 2008
Springer-Verlag New York Inc.
978-0-387-72489-8 (ISBN)
Springer-Verlag New York Inc.
978-0-387-72489-8 (ISBN)
Class field theory, the study of abelian extensions of algebraic number fields, is one of the largest branches of algebraic number theory. 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.
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.
This book is an accessible introduction to class field theory.
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.
A Brief Review.- Dirichlet#x2019;s Theorem on Primes in Arithmetic Progressions.- Ray Class Groups.- The Id#x00E8;lic Theory.- Artin Reciprocity.- The Existence Theorem, Consequences and Applications.- Local Class Field Theory.
| Reihe/Serie | Universitext |
|---|---|
| Zusatzinfo | X, 226 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| ISBN-10 | 0-387-72489-3 / 0387724893 |
| ISBN-13 | 978-0-387-72489-8 / 9780387724898 |
| Zustand | Neuware |
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