Class Field Theory

Cover
Title page
Preface
Chapter 1. Group and Field Theoretic Foundations
1. Infinite Galois Theory
2. Profinite Groups
3. G-Modules
4. The Herbrand Quotient
5. Kummer Theory
Chapter II. General Class Field Theory
1. Frobenius Elements and Prime Elements
2. The Reciprocity Map
3. The General Reciprocity Law
4. Class Fields
5. Infinite Extensions
Chapter III. Local Class Field Theory
1. The Class Field Axiom
2. The Local Reciprocity Law
3. Local Class Fields
4. The Norm Residue Symbol over Q_p
5. The Hilbert Symbol
6. Formal Groups
7. Fields of π^n-th Division Points
8. Higher Ramification Groups
9. The Weil Group
Chapter IV. Global Class Field Theory
1. Algebraic N umber Fields
2. Ideles and Idele Classes
3. Galois Extensions
4. Kummer Extensions
5. The Class Field Axiom
6. The Global Reciprocity Law
7. Global Class Fields
8. The Ideal- Theoretic Formulation of Class Field Theory
9. The Reciprocity Law of Power Residues
Chapter V. Zeta Functions and L-Series
1. The Riemann Zeta Function
2. The Dedekind Zeta Function
3. The Dirichlet L-Series
4. The Artin L-Series
5. The Equality of Dirichlet L-Series and Artin L-Series
6. Density Theorems
Literature
Index