局部域

　　The goal of this book is to present local class field theory from the cohomological point of view， following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions：primarily abelian：of "local" （i.e.， complete for a discrete valuation） fields with finite residue field. For example， such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts： the first two on the general theory of local fields， the third on group cohomology. Local class field theory， strictly speaking， does not appear until the fourth part.

暂缺《局部域》作者简介

Introduction
Leitfaden
Part One
LOCAL FIELDS (BASIC FACTS)
Part one LOCAL FIELDS (BASIC FACTS)
　Chapter I Discrete Valuation Rings and Dedekind Domains
　　1. Definition of Discrete Valuation Ring
　　2. Characterisations of Discrete Valuation Rings
　　3. De&kind Domains
　　4. Extensions
　　5. The Norm and Inclusion Homomorphisms
　　6. Example: Simple Extensions
　　7. Galois Extensions
　　8. Frobenius Substitution
　Chapter II Completion
　　1. Absolute Values and the Topology Defined by a Discrete Valuation
　　2. Extensions of a Complete Field
　　3. Extension and Completion
　　4. Strupture of complete discrecte valuation rings I:Equal characteristic case
5. Structure of complete discrete valuation rings II:Unequal characteristic case
6. Witt vectors
　　……
Chapter IV Ramification Groups
Chapter V The Norm
　Chapter VI Artin Representation
Part Three GROUP COHOMOLOGY
　Chapter VII Basic Facts
　Appendix Non-abelian Cohomology
　Chapter VIII Cohomology of Finite Groups
　Chapter IX Theorems of Tate and Nakayama
　Chapter X Galois Cohomology
　Chapter Xi Class Formations
Part Four LOCAL CALSS FIELD THEORY
　Chapter XII Brauer group of a local field
　Chapter XIII Local class field theory
　ChapterXIV Local symbols and Existence Theorem
Appendix The global case
Chater XV Ramification
Bibliography
Supplementary Bibliography for the English Edition