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 60
Pagina 3
... Arbitrary Fields 121 121 ... 122 124 125 129 130 131 131 5.2 . The Reduced Trace and Norm 132 5.3 . Splitting Fields 133 5.4 . The Brauer Group 133 5.5 . Simple Algebras over Local Fields 134 5.6 . The Structure of the Brauer Group of ...
... Arbitrary Fields 121 121 ... 122 124 125 129 130 131 131 5.2 . The Reduced Trace and Norm 132 5.3 . Splitting Fields 133 5.4 . The Brauer Group 133 5.5 . Simple Algebras over Local Fields 134 5.6 . The Structure of the Brauer Group of ...
Pagina 4
... Arbitrary Fields 2.2 . The Algebraic Closure of a Local Field 168 169 2.3 . The Maximal p - Extension of a Local Field 2.4 . The Galois Group of a Local Field ... 171 173 2.5 . The Maximal Algebraic Extension with Given Ramification 2.6 ...
... Arbitrary Fields 2.2 . The Algebraic Closure of a Local Field 168 169 2.3 . The Maximal p - Extension of a Local Field 2.4 . The Galois Group of a Local Field ... 171 173 2.5 . The Maximal Algebraic Extension with Given Ramification 2.6 ...
Pagina 8
... arbitrary number fields K : One has to define the notion of integral algebraic numbers . The integral algebraic numbers con- tained in K form a ring OK ( § 1.1 ) , which is the natural realm for the generaliza- tion of the unique ...
... arbitrary number fields K : One has to define the notion of integral algebraic numbers . The integral algebraic numbers con- tained in K form a ring OK ( § 1.1 ) , which is the natural realm for the generaliza- tion of the unique ...
Pagina 12
... arbitrary order in K is of the form D , : = Z [ ƒœ ] with a positive rational integer ƒ called the conductor of O ,. K Example 3. For number fields K of degree > 2 the maximal order Ok is not always of the form Z [ a ] . For instance ...
... arbitrary order in K is of the form D , : = Z [ ƒœ ] with a positive rational integer ƒ called the conductor of O ,. K Example 3. For number fields K of degree > 2 the maximal order Ok is not always of the form Z [ a ] . For instance ...
Pagina 16
... arbitrary positive real number c there is a number y Є such that lyl < c , \ NK / Q ( 7 ) ] < 2u2 . Proof . Let k be a natural number and ( k ) = { h1w1 + h2w2 | h , e Z , 0 ≤h , ≤ k for v = 1 , 2 } . By definition of u we have | 8 ...
... arbitrary positive real number c there is a number y Є such that lyl < c , \ NK / Q ( 7 ) ] < 2u2 . Proof . Let k be a natural number and ( k ) = { h1w1 + h2w2 | h , e Z , 0 ≤h , ≤ k for v = 1 , 2 } . By definition of u we have | 8 ...
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