| Chapter Ⅰ：Algebraic Integers 1. The Gaussian Integers 2. Integrality 3. Ideals 4. Lattices 5. Minkowski Theory 6. The Class Number 7. Dirichlet's Unit Theorem 8. Extensions of Dedekind Domains 9. Hilbert's Ramification Theory 10. Cyclotomic Fields 11. Localization 12. Orders 13. One-dimensional Schemes 14. Function Fields Chapter Ⅱ：The Theory of Valuations 1. The p-adic Numbers 2. The p-adic Absolute Value 3. Valuations 4. Completions 5. Local Fields 6. Henselian Fields 7. Unramified and Tamely Ramified Extensions 8. Extensions of Valuations 9. Galois Theory of Valuations 10. Higher Ramification Groups Chapter Ⅲ：Riemann-Roeh Theory 1. Primes 2. Different and Discriminant 3. Riemann-Roch 4. Metrized o-Modules 5. Grothendieck Groups 6. The Chern Character 7. Grothendieck-Riemann-Roch 8. The Euler-Minkow.ski Characteristic Chapter Ⅳ：Abstract Class Field Theory 1. Infinite Galois Theory 2. Projective and Inductive Limits 3. Abstract Galois Theory 4. Abstract Valuation Theory 5. The Reciprocity Map 6. The General Reciprocity Law 7. The Herbrand Quotient Chapter Ⅴ：Local Class Field Theory 1. The Local Reciprocity Law 2. The Norm Residue Symbol over Q（p） 3. The Hilbert Symbol 4. Formal Groups 5. Generalized Cyclotomic Theory 6. Higher Ramification Groups Chapter Ⅵ：Global Class Field Theory 1. Idèles and Idèle Classes 2. Idèles in Field Extensions 3. The Herbrand Quotient of the Idèle Class Group 4. The Class Field Axiom 5. The Global Reciprocity Law 6. Global Class Fields 7. The Ideal-Theoretic Version of Class Field Theory 8. The Reciprocity Law of the Power Residues Chapter Ⅶ：Zeta Functions and L-series 1. The Riemann Zeta Function 2. Dirichlet L-series 3. Theta Series 4. The Higher-dimensional Gamma Function 5. The Dedekind Zeta Function 6. Hecke Characters 7. Theta Series of Algebraic Number Fields 8. Hecke L-series 9. Values of Dirichlet L-series at Integer Points 10. Artin L-series 11. The Artin Conductor 12. The Functional Equation of Artin L-series 13. Density Theorems Bibliography Index |
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