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Class field theory : from theory to practice /

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Bibliographic Details
Main Author: Gras, Georges, 1944-
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin ; New York : Springer, [2003]
Series:Springer monographs in mathematics.
Subjects:
Class field theory.
Corps de classe.
Klassenkörpertheorie.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Introduction to Global Field Theory
  • I. Basic Tools and Notations
  • 1. Places of K
  • 2. Embeddings of a Number Field in its Completions
  • 3. Number and Ideal Groups
  • 4. Idele Groups
  • Generalized Class Groups
  • 5. Reduced Ideles
  • Topological Aspects
  • 6. Kummer Extensions
  • II. Reciprocity Maps
  • Existence Theorems
  • 1. The Local Reciprocity Map
  • Local Class Field Theory
  • 2. Idele Groups in an Extension L/K
  • 3. Global Class Field Theory: Idelic Version
  • 4. Global Class Field Theory: Class Group Version
  • 5. Ray Class Fields
  • Hilbert Class Fields
  • 6. The Hasse Principle
  • For Norms
  • For Powers
  • 7. Symbols Over Number Fields
  • Hilbert and Regular Kernels