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 48
Pagina 4
... Extensions with Prescribed Local Behavior 186 188 188 3.6 . Realization of Extensions with Prescribed Galois Group by Means of Hilbert's Irreducibility Theorem 190 Chapter 4. Abelian Fields 192 § 1. The Integers of 4 Contents.
... Extensions with Prescribed Local Behavior 186 188 188 3.6 . Realization of Extensions with Prescribed Galois Group by Means of Hilbert's Irreducibility Theorem 190 Chapter 4. Abelian Fields 192 § 1. The Integers of 4 Contents.
Pagina 5
... Integers of an Abelian Field 193 1.1 . The Coordinates 193 1.2 . The Galois 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 ...
... Integers of an Abelian Field 193 1.1 . The Coordinates 193 1.2 . The Galois 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 ...
Pagina 7
... integers , Q for the field of rational numbers , R for the field of real numbers , and C for the field of complex numbers . For any ring with unit element , * denotes the group of units , i.e. the group of invertible elements and 4 ...
... integers , Q for the field of rational numbers , R for the field of real numbers , and C for the field of complex numbers . For any ring with unit element , * denotes the group of units , i.e. the group of invertible elements and 4 ...
Pagina 8
... integers by f ( a1 , a2 ) with a1 , a2 € Z can be reformulated as a question of factorization of algebraic numbers of the form a1 + √Da2 . These numbers form a module in the field Q ( D ) . ... - Beginning with the year 1840 Kummer ...
... integers by f ( a1 , a2 ) with a1 , a2 € Z can be reformulated as a question of factorization of algebraic numbers of the form a1 + √Da2 . These numbers form a module in the field Q ( D ) . ... - Beginning with the year 1840 Kummer ...
Pagina 10
... integers a1 , ... , a , for some s such that as + a1as − 1 + k + as 0 . K K ( 1.1 ) Furthermore we shall see in §2 that Ox is the natural generalization of Z in the sense that it is possible to develop arithmetic in Ok . The elements ...
... integers a1 , ... , a , for some s such that as + a1as − 1 + k + as 0 . K K ( 1.1 ) Furthermore we shall see in §2 that Ox is the natural generalization of Z in the sense that it is possible to develop arithmetic in Ok . The elements ...
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