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 46
Pagina 1
... Discriminant 3.6 . Inessential Discriminant Divisors 3.7 . Normal Extensions 3.8 . Ideals in Algebraic Number Fields 3.9 . Cyclotomic Fields 3.10 . Application to Fermat's Last Theorem I 29 30 30 33 36 36 40 41 43 §4 . Valuations 4.1 ...
... Discriminant 3.6 . Inessential Discriminant Divisors 3.7 . Normal Extensions 3.8 . Ideals in Algebraic Number Fields 3.9 . Cyclotomic Fields 3.10 . Application to Fermat's Last Theorem I 29 30 30 33 36 36 40 41 43 §4 . Valuations 4.1 ...
Pagina 2
... Discriminant Estimation Chapter 2. Class Field Theory 90 § 1. The Main Theorems of Class Field Theory 92 1.1 . Class Field Theory for Abelian Extensions of Q 1.2 . The Hilbert Class Field 92 93 1.3 . Local Class Field Theory 93 1.4 ...
... Discriminant Estimation Chapter 2. Class Field Theory 90 § 1. The Main Theorems of Class Field Theory 92 1.1 . Class Field Theory for Abelian Extensions of Q 1.2 . The Hilbert Class Field 92 93 1.3 . Local Class Field Theory 93 1.4 ...
Pagina 4
... Discriminant Estimation from Above Characterization of an Algebraic Number Field by its Galois Group §3 . Extensions with Given Galois Groups 3.2 . Embedding Problems for Local and Global Fields 181 182 182 183 185 3.3 . Extensions with ...
... Discriminant Estimation from Above Characterization of an Algebraic Number Field by its Galois Group §3 . Extensions with Given Galois Groups 3.2 . Embedding Problems for Local and Global Fields 181 182 182 183 185 3.3 . Extensions with ...
Pagina 9
... discriminant and the theory of ramification groups . Nowadays algebraic number fields are mostly studied by a mixture of ideal and valuation theory . The latter , being the third method mentioned above , is presented in §4 . p - adic ...
... discriminant and the theory of ramification groups . Nowadays algebraic number fields are mostly studied by a mixture of ideal and valuation theory . The latter , being the third method mentioned above , is presented in §4 . p - adic ...
Pagina 11
... discriminant of m and is denoted by d ( m ) . ... , Let ẞ1 , ... , ẞn be a basis of O ( m ) and let A e GL „ ( Q ) such that ᏰᎢ ( 1 , ... , n ) T = A ( Bí , ... , Ba ) . Then the absolute value [ det A of the determinant of A is ...
... discriminant of m and is denoted by d ( m ) . ... , Let ẞ1 , ... , ẞn be a basis of O ( m ) and let A e GL „ ( Q ) such that ᏰᎢ ( 1 , ... , n ) T = A ( Bí , ... , Ba ) . Then the absolute value [ det A of the determinant of A is ...
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