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 82
Pagina 3
... Proof of the Main Theorems of Class Field Theory 4.1 . Application of the Theorem of Tate to Class Field Theory 4.2 . Class Formations 4.3 . Cohomology of Local Fields 4.4 . Cohomology of Ideles and Idele Classes 4.5 . Analytical Proof ...
... Proof of the Main Theorems of Class Field Theory 4.1 . Application of the Theorem of Tate to Class Field Theory 4.2 . Class Formations 4.3 . Cohomology of Local Fields 4.4 . Cohomology of Ideles and Idele Classes 4.5 . Analytical Proof ...
Pagina 7
... Proofs , or Exercises stands the signor . The sign means that the Theorem , Proposition , Lemma , or Exercise is easy to prove or that we gave a full sketch of the proof . The sign means that one needs for the proof ideas which are not ...
... Proofs , or Exercises stands the signor . The sign means that the Theorem , Proposition , Lemma , or Exercise is easy to prove or that we gave a full sketch of the proof . The sign means that one needs for the proof ideas which are not ...
Pagina 10
... Proof . Let a be an algebraic integer in K. Then we can take for m the module generated by 1 , α , a2 , ... , a " -1 where n : = [ K : Q ] . On the other hand if we have am < m for some a Є K and μ1 , ... , μ , is a basis of m , then ...
... Proof . Let a be an algebraic integer in K. Then we can take for m the module generated by 1 , α , a2 , ... , a " -1 where n : = [ K : Q ] . On the other hand if we have am < m for some a Є K and μ1 , ... , μ , is a basis of m , then ...
Pagina 14
... Proof . We apply Minkowski's convex body theorem to an M and the lattice to ( m ) where t > 0 is determined by V ( M ) = ( 2t ) " 2 ̄ * 2√ / \ d ( m ) | . Then the assumptions of the theorem are fulfilled . Hence there is an element to ...
... Proof . We apply Minkowski's convex body theorem to an M and the lattice to ( m ) where t > 0 is determined by V ( M ) = ( 2t ) " 2 ̄ * 2√ / \ d ( m ) | . Then the assumptions of the theorem are fulfilled . Hence there is an element to ...
Pagina 15
... proof of the following discriminant theorem of Hermite : Theorem 1.12 . Let N be a natural number . There are only ... proof of Theorem 1.13 proceeds in several steps . a ) Let 91 , ... , 9 , be as in the proof of Theorem 1.10 and put l ...
... proof of the following discriminant theorem of Hermite : Theorem 1.12 . Let N be a natural number . There are only ... proof of Theorem 1.13 proceeds in several steps . a ) Let 91 , ... , 9 , be as in the proof of Theorem 1.10 and put l ...
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