دانلود کتاب Profinite Groups, Arithmetic, and Geometry. (AM-67), Volume 67

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CONTENTS\nPREFACE\nCHAPTER I – PROFINITE GROUPS\n §0. Preliminaries on Projective and Inductive Limits\n §1. Profinite Groups\n §2. Supernatural Numbers and the Sylow Theory\nCHAPTER II – COHOMOLOGY OF PROFINITE GROUPS\n §1. δ-functors and the Definition of the Cohomology of Profinite Groups\n §2. Behavior of the Cohomology as a Functor, Induced Modules\n §3. Restriction, Transfer (co-restriction), and Cup-products\n §4. A Utilitarian View of Spectral Sequences\nCHAPTER III – COHOMOLOGICAL DIMENSION\n §1. Definition and Elementary Properties\n §2. The Case of Cohomological Dimension One\n §3. The Structure of Profinite p-groups; Šafarevič-Golod’s Theorem\n §4. Šafarevič’s Solution of the Class Tower Problem\nCHAPTER IV – GALOIS COHOMOLOGY AND FIELD THEORY\n §1. Resume of Krull\'s Galois Theory and First Results\n §2. The Cohomological Dimension of Fields\n §3. Algebraic Dimension, Quasi-algebraic Closure, and the Property Cr\n §4. Existence of Fields of Arbitrary Cohomological Dimension\n §5. Counter-examples in the Theory of Cohomological Dimension and Forms\nCHAPTER V – LOCAL CLASS FIELD THEORY\n §1. Local Fields and Their Extensions – A Resumé\n §2. Cohomological Triviality, Tate and Nakayama Theorems, and Herbrand Quotients\n §3. The Brauer Group of a Local Field\n §4. The Existence Theorem (Part I: Formal Existence Theorem, and beginning of the proof.)\n §5. The Existence Theorem (Part II: The Hilbert Symbols and completion of the proof.)\nCHAPTER VI – DUALITY\n §1. Dualizing Modules and Poincaré Groups\n §2. Grothendieck Topologies and Cohomology\n §3. Galois, Étale, and Flat Cohomology\n §4. Finite Group Schemes and Their Cohomology Over a Local Field\n §5. Tate-Nakayama Duality\n §6. Duality Theorem for Finite Group Schemes\nBIBLIOGRAPHY