Class Field Theory

• Main Author: Childress, Nancy. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Universitext
• Subjects: Mathematics.; Field theory (Physics).; Number theory.; Field Theory and Polynomials.; Number Theory.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-72490-4

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 Che...

Table of Contents:

• Preface
• A Brief Review
• Dirichlet's Theorem on Primes in Arithmetic Progressions
• Ray Class Groups
• The Idelic Theory
• Artin Reciprocity
• The Existence Theorem, Consequences and Applications
• Local Class Field Theory
• Bibliography
• Index.