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Galois Cohomology and Class Field Theory

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Cover of 'Galois Cohomology and Class Field Theory'

Table of Contents

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    Book Overview
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    Chapter 1 Cohomology of Finite Groups: Basic Properties
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    Chapter 2 Groups Modified à la Tate, Cohomology of Cyclic Groups
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    Chapter 3 p -Groups, the Tate–Nakayama Theorem
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    Chapter 4 Cohomology of Profinite Groups
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    Chapter 5 Cohomological Dimension
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    Chapter 6 First Notions of Galois Cohomology
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    Chapter 7 Basic Facts About Local Fields
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    Chapter 8 Brauer Group of a Local Field
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    Chapter 9 Local Class Field Theory: The Reciprocity Map
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    Chapter 10 The Tate Local Duality Theorem
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    Chapter 11 Local Class Field Theory: Lubin–Tate Theory
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    Chapter 12 Basic Facts About Global Fields
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    Chapter 13 Cohomology of the Idèles: The Class Field Axiom
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    Chapter 14 Reciprocity Law and the Brauer–Hasse–Noether Theorem
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    Chapter 15 The Abelianised Absolute Galois Group of a Global Field
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    Chapter 16 Class Formations
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    Chapter 17 Poitou–Tate Duality
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    Chapter 18 Some Applications
Attention for Chapter 8: Brauer Group of a Local Field
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