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 85
Pagina 1
... Modules and Orders Module Classes 7 8 9 10 12 1.3 . The Unit Group of an Order 15 The Unit Group of a Real - Quadratic Number Field 1.5 . Integral Representations of Rational Numbers by Complete 17 Forms 18 1.6 . Binary Quadratic Forms ...
... Modules and Orders Module Classes 7 8 9 10 12 1.3 . The Unit Group of an Order 15 The Unit Group of a Real - Quadratic Number Field 1.5 . Integral Representations of Rational Numbers by Complete 17 Forms 18 1.6 . Binary Quadratic Forms ...
Pagina 4
... Modules 155 1.7 . Inductive Limits in C 156 1.8 . Galois Theory of Infinite Algebraic Extensions 157 1.9 . Cohomology of Profinite Groups 159 1.10 . Cohomological Dimension 159 1.11 . The Dualizing Module 160 1.12 . Cohomology of Pro ...
... Modules 155 1.7 . Inductive Limits in C 156 1.8 . Galois Theory of Infinite Algebraic Extensions 157 1.9 . Cohomology of Profinite Groups 159 1.10 . Cohomological Dimension 159 1.11 . The Dualizing Module 160 1.12 . Cohomology of Pro ...
Pagina 5
... Module Structure of the Ring of Integers of an Abelian Field 194 §2 . The Arithmetical Class Number Formula 195 2.1 . The Arithmetical Class Number Formula for Complex Abelian Fields 195 ... 2.2 . The Arithmetical Class Number Formula ...
... Module Structure of the Ring of Integers of an Abelian Field 194 §2 . The Arithmetical Class Number Formula 195 2.1 . The Arithmetical Class Number Formula for Complex Abelian Fields 195 ... 2.2 . The Arithmetical Class Number Formula ...
Pagina 8
... module in the field Q ( D ) . ... - Beginning with the year 1840 Kummer ( 1975 ) considered the ring of numbers of ... modules of elements in K appear in connection with decomposible forms ( § 1.5-6 ) . Therefore we begin Chap . 1 with ...
... module in the field Q ( D ) . ... - Beginning with the year 1840 Kummer ( 1975 ) considered the ring of numbers of ... modules of elements in K appear in connection with decomposible forms ( § 1.5-6 ) . Therefore we begin Chap . 1 with ...
Pagina 10
... modules in K : In this paragraph a module m in K means a finitely generated subgroup of K. Since the group K✶ has no torsion , m is a free Z - module of rank < [ K : Q ] . The module m is called complete ( or a lattice in K ) if its ...
... modules in K : In this paragraph a module m in K means a finitely generated subgroup of K. Since the group K✶ has no torsion , m is a free Z - module of rank < [ K : Q ] . The module m is called complete ( or a lattice in K ) if its ...
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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Parole e frasi comuni
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