1 A Brief Review 1 Number Fields 2 Completions of Number Fields 3 Some General Questions Motivating Class Field Theory 2 Dirichlet's Theorem on Primes in Arithmetic Progressions 1 Characters of Finite Abelian Groups 2 Dirichlet Characters 3 Dirichlet Series 4 Dirichlet's Theorem on Primes in Arithmetic Progressions 5 Dirichlet Density 3 Ray Class Groups 1 The Approximation Theorem and Infinite Primes 2 Ray Class Groups and the Universal Norm Index Inequality 3 The Main Theorems of Class Field Theory 4 The Idelie Theory 1 Places of a Number Field 2 A Little Topology 3 The Group of Ide1es of a Number Field 4 Cohomology of Finite Cyclic Groups and the Herbrand Quotient 5 Cyclic Galois Action on Ideles 5 Artin Reciprocity 1 The Conductor of an Abelian Extension of Number Fields and the Artin Symbol 2 Artin Reciprocity 3 An Example: Quadratic Reciprocity 4 Some Preliminary Results about the Artin Map on Local Fields 6 The Existence Theorem, Consequences and Applications l The Ordering Theorem and the Reduction Lemma 2 Kummer n-extensions and the Proof of the Existence Theorem 3 The Artin Map on Local Fields 4 The Hilbert Class Field 5 Arbitrary Finite Extensions of Number Fields 6 Infinite Extensions and an Alternate Proof of the Existence Theorem. 7 An Example: Cyclotomic Fields 7 Local Class Field Theory 1 Some Preliminary Facts About Local Fields 2 A Fundamental Exact Sequence 3 Local Units Modulo Norms 4 One-Dimensional Formal Group Laws 5 The Formal Group Laws of Lubin and Tare 6 Lubin-Tate Extensions 7 The Local Artin Map Bibliography Index
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