Algebraic Number Theory

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Springer Science & Business Media, 6 dic 2012 - 269 pagine
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From the reviews: "... 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
"... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995

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Sommario

Preface
7
Number Fields
19
3 Dedekind Rings
28
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
2 Complex Multiplication
107
2 Galois Cohomology of Local and Global Fields
168
Abelian Fields
192
3 Iwasawas Theory of IExtensions
206
4 padic LFunctions
212
Artin LFunctions and Galois Module Structure
219
2 Galois Module Structure and Artin Root Numbers
234
Fields Domains and Complexes
237
Tables
245

5 Simple Algebras
131
6 Explicit Reciprocity Laws and Symbols
137
7 Further Results of Class Field Theory
145
Cohomology of Profinite Groups
151
References
251
Author Index 263
262
Copyright

Altre edizioni - Visualizza tutto

Algebraic Number Theory, Volume 62
H. Koch,Helmut Koch
Anteprima limitata - 1997
Algebraic Number Theory
H. Koch
Anteprima non disponibile - 1997

Parole e frasi comuni

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

Informazioni sull'autore (2012)

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 di Encyclopaedia of Mathematical Sciences
AutoreH. Koch
CuratoriA.N. Parshin, I.R. Shafarevich
Edizioneillustrata
EditoreSpringer Science & Business Media, 2012
ISBN3642580955, 9783642580956
Lunghezza269 pagine
  
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