Algebraic Number TheorySpringer Science & Business Media, 6 dic 2012 - 269 pagine 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 |
Dall'interno del libro
Risultati 1-5 di 33
Pagina 2
... adic Number Field Extension of Valuations 4.4 . 4.5 . 4.6 . Finite Extensions of p - adic Number Fields 4.7 . Kummer Extensions 45 45 49 49 51 53 55 58 59 60 62 63 64 .... 65 689 66 68 69 70 74 76 77 79 80 82 84 85 87 87 88 4.8 ...
... adic Number Field Extension of Valuations 4.4 . 4.5 . 4.6 . Finite Extensions of p - adic Number Fields 4.7 . Kummer Extensions 45 45 49 49 51 53 55 58 59 60 62 63 64 .... 65 689 66 68 69 70 74 76 77 79 80 82 84 85 87 87 88 4.8 ...
Pagina 3
... p - adic Number Fields 143 • 6.6 . Tame and Wild Symbols 144 6.7 . Remarks about Milnor's K - Theory 144 7.1 . 7.2 . §7 . Further Results of Class Contents 3.
... p - adic Number Fields 143 • 6.6 . Tame and Wild Symbols 144 6.7 . Remarks about Milnor's K - Theory 144 7.1 . 7.2 . §7 . Further Results of Class Contents 3.
Pagina 5
... p - adic L - Functions 4.1 . The Hurwitz Zeta Function 4.2 . p - adic L - Functions 207 208 209 211 212 213 4.3 . Congruences for Bernoulli Numbers 214 4.4 . Generalization to Totally Real Number Fields 215 4.5 . The p - adic Class ...
... p - adic L - Functions 4.1 . The Hurwitz Zeta Function 4.2 . p - adic L - Functions 207 208 209 211 212 213 4.3 . Congruences for Bernoulli Numbers 214 4.4 . Generalization to Totally Real Number Fields 215 4.5 . The p - adic Class ...
Pagina 9
... p - adic analysis , which is an essential part of the valuation theoretic method , is developed in this article only so far as it is needed in the following . § 5 explains harmonic analysis in local and global fields and §6 is devoted ...
... p - adic analysis , which is an essential part of the valuation theoretic method , is developed in this article only so far as it is needed in the following . § 5 explains harmonic analysis in local and global fields and §6 is devoted ...
Pagina 49
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Sommario
7 | |
22 | |
3 Dedekind Rings | 28 |
60 | 42 |
69 | 49 |
76 | 56 |
Harmonic Analysis on Local and Global Fields | 63 |
6 Hecke LSeries and the Distribution of Prime Ideals | 70 |
7 Further Results of Class Field Theory | 145 |
Cohomology of Profinite Groups | 151 |
2 Galois Cohomology of Local and Global Fields | 168 |
Abelian Fields | 192 |
3 Iwasawas Theory of IExtensions | 206 |
Artin LFunctions and Galois Module Structure | 219 |
2 Galois Module Structure and Artin Root Numbers | 234 |
Fields Domains and Complexes | 237 |
Class Field Theory | 90 |
2 Complex Multiplication | 107 |
Simple Algebras | 131 |
6 Explicit Reciprocity Laws and Symbols | 137 |
Tables | 245 |
References | 251 |
Author Index 263 | 262 |
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a₁ abelian extension abelian field abelian group algebraic number field arbitrary Artin automorphism called Chap class field theory closed subgroup cohomology complex conductor conjecture corresponding cyclic Dedekind ring defined denotes Dirichlet discriminant divisor theory exact sequence Example extension L/K extension of Q finite extension finite group finite normal extension following theorem function G-module G₁ Galois group global fields group G H¹(G H²(G Hasse Hecke character Hence Hilbert homomorphism ideal class group idele imaginary-quadratic implies induces infinite places integers irreducible isomorphism L-functions Lemma Let G Let L/K Main reference module morphism natural number norm symbol normal extension normal subgroup number theory polynomial prime divisors prime element prime ideal prime numbers principal ideal pro-p-group profinite group Proposition quadratic r₂ ramified reciprocity law representation resp roots of unity Shafarevich simple algebra subgroup of G trivial U₁ unramified valuation Z/pZ