1986•Medical Entomology and ZoologyRequires access
Class Field Theory
Jürgen Neukirch
Open publisher page 165 citations
Abstract
I. Group and Field Theoretic Foundations.- 1. Infinite Galois Theory.- 2. Profinite Groups.- 3. G-Modules.- 4. The Herbrand Quotient.- 5. Kummer Theory.- 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.- 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 Qp.- 5. The Hilbert Symbol.- 6. Formal Groups.- 7. Fields of ?n-th Division Points.- 8. Higher Ramification Groups.- 9. The Weil Group.- IV. Global Class Field Theory.- 1. Algebraic Number 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.- 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.