Algebraic Number Theory, Volume 62

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Springer Science & Business Media, 12 set 1997 - 269 pagine
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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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Pagine selezionate

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

Altre edizioni - Visualizza tutto

Algebraic Number Theory
H. Koch
Anteprima limitata - 2012
Algebraic Number Theory
H. Koch
Anteprima non disponibile - 1997

Parole e frasi comuni

abelian extension algebraic number field application arbitrary Artin basis called Chap character class field theory class group class number closed cohomology complex compute conductor conjecture consider contains continuous corresponding cyclic cyclic extension cyclotomic defined definition denotes determined dimension direct discriminant divisor elements embedding equal equation exact Example exists factor finite finite extension fixed formula function Furthermore G-module Galois group given global Hence Hilbert homomorphism implies induces infinite integers irreducible isomorphism L-functions Let G Main reference maximal means module morphism multiplication natural number norm normal extension p-adic places polynomial prime ideal principal pro-p-group problem profinite group Proof properties Proposition proved quadratic ramified representation residue resp respect ring roots of unity sequence shows structure subgroup symbol Theorem trivial unique unit unramified valuation values

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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.

Informazioni bibliografiche

QR code for Algebraic Number Theory
TitoloAlgebraic Number Theory, Volume 62
Algebraic Number Theory
Volume 62 di Encyclopaedia of Mathematical Sciences
AutoriH. Koch, Helmut Koch
CuratoriA.N. Parshin, I.R. Shafarevich
Edizioneillustrata, ristampa
EditoreSpringer Science & Business Media, 1997
ISBN3540630031, 9783540630036
Lunghezza269 pagine
  
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