Algebraic Number Theory, Volume 62

Copertina anteriore
Springer Science & Business Media, 12 set 1997 - 269 pagine
From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences:

"... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes."
Monatshefte fuer Mathematik, 1994
"... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians."
Acta Scientiarum Mathematicarum, 1993
 

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Sommario

Basic Number Theory
8
1 Orders in Algebraic Number Fields
9
2 Rings with Divisor Theory
22
3 Dedekind Rings
27
4 Valuations
45
5 Harmonic Analysis on Local and Global Fields
63
6 Hecke LSeries and the Distribution of Prime Ideals
70
Class Field Theory
90
3 Extensions with Given Galois Groups
182
Abelian Fields
192
1 The Integers of an Abelian Field
193
2 The Arithmetical Class Number Formula
195
3 Iwasawas Theory of ΓExtensions
206
4 padic LFunctions
211
Artin LFunctions and Galois Module Structure
219
1 Artin LFunctions
222

1 The Main Theorems of Class Field Theory
92
2 Complex Multiplication
107
3 Cohomology of Groups
112
4 Proof of the Main Theorems of Class Field Theory
121
5 Simple Algebras
131
6 Explicit Reciprocity Laws and Symbols
137
7 Further Results of Class Field Theory
145
Galois Groups
150
1 Cohomology of Profinite Groups
151
2 Galois Cohomology of Local and Global Fields
168
2 Galois Module Structure and Artin Root Numbers
234
Fields Domains and Complexes
237
Quadratic Residues
240
Locally Compact Groups
241
Bernoulli Numbers
243
Tables
245
References
251
Author Index
263
Subject Index
266
Copyright

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Informazioni sull'autore (1997)

Igor Rostislavovich Shafarevich was born in Zhitomir, Ukraine on June 3, 1923. He graduated from Moscow State University with a specialty in astronomy. He taught at Moscow State University for more than 30 years. He was an internationally renowned mathematician who played a central role in the anti-Soviet dissident movement during the Cold War. His textbooks on algebraic geometry were translated into English and regarded as classics in the field. He also wrote The Socialist Phenomenon and contributed essays to From Under the Rubble. He died on February 19, 2017 at the age of 93.

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