Class Field Theory Ams Chelsea Publishing Second Edition by Emil Artin And John Tate ISBN 978-0821844267 0821844261
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Product details:
ISBN 10: 0821844261
ISBN 13: 978-0821844267
Author: Emil Artin And John Tate
This classic book, originally published in 1968, is based on notes of a year-long seminar the authors ran at Princeton University. The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory, and the authors accomplished this goal spectacularly: for more than 40 years since its first publication, the book has served as an ultimate source for many generations of mathematicians. In this revised edition, two mathematical additions complementing the exposition in the original text are made. The new edition also contains several new footnotes, additional references, and historical comments.
Table of contents:
Preliminaries
1. Idèles and Idèle Classes
2. Cohomology
3. The Herbrand Quotient
4. Local Class Field Theory
Chapter V. The First Fundamental Inequality
1. Statement of the First Inequality
2. First Inequality in Function Fields
3. First Inequality in Global Fields
4. Consequences of the First Inequality
Chapter VI. Second Fundamental Inequality
1. Statement and Consequences of the Inequality
2. Kummer Theory
3. Proof in Kummer Fields of Prime Degree
4. Proof in p-extensions
5. Infinite Divisibility of the Universal Norms
6. Sketch of the Analytic Proof of the Second Inequality
Chapter VII. Reciprocity Law
1. Introduction
2. Reciprocity Law over the Rationals
3. Reciprocity Law
4. Higher Cohomology Groups in Global Fields
Chapter VIII. The Existence Theorem
1. Existence and Ramification Theorem
2. Number Fields
3. Function Fields
4. Decomposition Laws and Arithmetic Progressions
Chapter IX. Connected Component of Idèle Classes
1. Structure of the Connected Component
2. Cohomology of the Connected Component
Chapter X. The Grunwald-Wang Theorem
1 Interconnection between Local and Global m-th Powers
2. Abelian Fields with Given Local Behavior
3. Cyclic Extensions
Chapter XI. Higher Ramification Theory
1. Higher Ramification Groups
2. Ramification Groups of a Subfield
3. The General Residue Class Field
4. General Local Class Field Theory
5. The Conductor
Appendix: Induced Characters
Chapter XII. Explicit Reciprocity Laws
1. Formalism of the Power Residue Symbol
2. Local Analysis
3. Computation of the Norm Residue Symbol in Certain Local Kummer Fields
4. The Power Reciprocity Law
Chapter XIII. Group Extensions
1. Homomorphisms of Group Extensions
2. Commutators and Transfer in Group Extensions
3. The Akizuki-Witt Map v: H²(G,A) → H²(G/H,A”)
4. Splitting Modules and the Principal Ideal Theorem
Chapter XIV. Abstract Class Field Theory
1 Formations
2. Field Formations. The Brauer Groups
3. Class Formations; Method of Establishing Axioms
4. The Main Theorem
Exercise
5. The Reciprocity Law Isomorphism
6. The Abstract Existence Theorem
Chapter XV. Weil Groups
Bibliography
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Tags: Emil Artin And John Tate, Class Field, Theory Ams