Neukrich J. — Algebraic number theory :: Электронная библиотека попечительского совета мехмата МГУ

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Neukrich J. — Algebraic number theory

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Название: Algebraic number theory

Автор: Neukrich J.

Аннотация:

From the review: "The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner... The author discusses the classical concepts from the viewpoint of Arakelov theory.... The treatment of class field theory is ... particularly rich in illustrating complements, hints for further study, and concrete examples.... The concluding chapter VII on zeta-functions and L-series is another outstanding advantage of the present textbook.... The book is, without any doubt, the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available."
W. Kleinert in: Zentralblatt für Mathematik, 1992

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 588

Добавлена в каталог: 14.09.2007

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Предметный указатель

Factorial ring      7
Faltings, theorem of (Mordell conjecture)      207
Fermat's last theorem      37 38
Fesenko, I.      310
Fibonacci numbers      53
Finite prime (place)      183
Finiteness of class number      36 81
Fontaine, J.M., theorem of      207
Formal $\mathcal{O}$ -module      343
Formal group      342
Formal group, division points of      347
Formal group, logarithm of      343 345
Fourier transform      446
Fractional ideal      21
Frey, G.      38
Frobenius, abstract      285 287
Frobenius, automorphism      58 286 406
Frobenius, correspondence      226
Frobenius, on Witt vectors      134
Frobenius, reciprocity      521
Function field      94
Functional equation, Artin L-series      540 541
Functional equation, Dedekind zeta function      467
Functional equation, Dirichlet L-series      440
Functional equation, Hecke L-series      502 503
Functional equation, Mellin transform      422
Functional equation, Riemann's zeta function      425 426
Fundamental group      93
Fundamental group of a G-set      307
Fundamental identity for prime ideals      46
Fundamental identity of valuation theory      150 155 165
Fundamental mesh of a lattice      24
Fundamental mesh, regulator      43 431 443
Fundamental mesh, volume of the fundamental mesh      26
Fundamental mesh, volume of the fundamental mesh of a replete ideal      212
Fundamental mesh, volume of the fundamental mesh of an ideal      31
Fundamental mesh, volume of the fundamental mesh of the unit lattice      43
Fundamental units      42
Furtwangler, P.      406 413
G-modulation      307
G-module      276
G-module, induced      312 374
Galois descent      372
Galois group, absolute      261
Galois theory of valuations      166
Galois theory, abstract      275
Galois theory, infinite      261
Gamma function      421
Gamma function, higher-dimensional      454
Gauss sum      51 438 473 488
Gauss's reciprocity law      51 64 416
Gaussian integers      1
Gaussian prime numbers      3
Gaussian units      3
General reciprocity law      300
Generalized cyclotomic theory      346
Generic point      86
Genus of a number field      214 467
Genus of a Riemann surface      209
Ghost components of Witt vectors      134
Global class field      395
Global class field, axiom      383
Global class field, theory      357 390
Global field      134
Global norm residue symbol      391
Global reciprocity law      390
Global Tate duality      404
Golod — Safarevic      413
Groebencharacter      436 470
Groebencharacter, conductor of      473
Groebencharacter, exponent of      478
Groebencharacter, primitive      472
Groebencharacter, type of      478
Grothendieck group, replete      233
Grothendieck — Riemann — Roch      254
Grothendieck, A.      225 253
Group cohomology      284
Grunwald, theorem of      405
Gysin map      253
Haar measure on $\mathbb{R}$       446
Haar measure on a $\mathfrak{p}$ -adic number field      142
Hasse norm theorem      384
Hasse — Arf, theorem of      355 530
Hasse — Minkowski, theorem of      385
Hasse's Zahlbericht      363
Hecke character      480
Hecke L-series      493 496 497
Hecke L-series, completed      499 503
Hecke L-series, functional equation      502 503
Hecke L-series, Hecke and Artin L-series      539
Hecke L-series, partial      496
Hecke theta series      489
Hecke theta series, partial      489
Hecke theta series, transformation formula      490
Hensel's lemma      129 148
Hensel, K.      99
Henselian, field      143 147
Henselian, local ring      152
Henselian, P-valuation      298
Henselian, valuation      143 288 309 389
Henselization      143
Herbrand, quotient      312 378
Herbrand, theorem of      180
Hermite, theorem of      206
Hermitian scalar product      28 226 444
Higher ramification groups      176 352
Higher unit group      122
Higher-dimensional class field theory      310
Higher-dimensional gamma function      454
Higher-dimensional logarithm      445
Hilbert 90      278 281 283 284
Hilbert class field      399 400 402
Hilbert symbol      305 333 414
Hilbert symbol, explicit      339
Hilbert symbol, product formula      414
Hilbert symbol, tame      335
Hilbert — Noether, theorem of      283
Hilbert's ramification theory      53 166
Hilbert, D.      53
Hurwitz formula      220
Ideal      16
Ideal class group      22 186
Ideal class group, replete      186
Ideal group      21 408
Ideal group, defined $mod \mathfrak{m}$       408
Ideal number      16 486
Ideal, absolute norm of      34
Ideal, degree of a replete ideal      213
Ideal, discriminant of      14
Ideal, dual      194
Ideal, fractional      21
Ideal, integral      21
Ideal, invertible      74
Ideal, norm of      186
Ideal, principal ideal theorem      410
Ideal, replete ideal      185
Ideal, replete principal ideal      186
Ideal, volume of fundamental mesh      31 212
Idele      357
Idele, absolute norm of      361
Idele, idele class group      359
Idele, idele group      357
Idele, norm of      370
Idele, principal      359
Idele, S-idele      358
Imaginary quadratic field      402
Index of specialty      218
Induced character      521
Induced G-module      312 374 521
Induced representation      521

Inductive limit      266
Inductive system      265
Inertia degree      46 49 184 285
Inertia degree of a metrized number field      224
Inertia degree of a prime ideal      46 49
Inertia degree of a primes (place)      184
Inertia degree of a valuation      150 165
Inertia degree, abstract      285 309
Inertia field of a prime ideal      57
Inertia field of a valuation      173
Inertia group of a prime ideal      57
Inertia group of a valuation      168
Inertia group, abstract      285
Infinite Galois theory      261
Infinite prime      183
Infinite prime number      184
Integer, algebraic      5
Integer, Gaussian      1
Integer, p-adic      100 104 111
Integral, basis      12
Integral, closure      7
Integral, ideal      21
Integral, integrally closed      7
Integral, ring extension      6
Inverse different      195
Invertible $\mathcal{O}$ -module      229 230
Invertible ideal      74
Irreducible character      520
Irreducible representation      519
Irregular prime number      38
Isometric      229
Iwasawa theory      63
Iwasawa, K.      37
J-invariant      402
Jacobi symbol      417
Jacobi's theta series      422 424
Jannsen U.      221
K-theory      193 310 431
Kahler differentials      200
Kahler, E.      200
Kato, K.      310 432
Krasner's Lemma      152
Kronecker — Weber Theorem      324 398
Kronecker's Jugendtraum      401
Kronecker's programme      548
Krull dimension      73
Krull topology      167 262
Krull valuation      123
Krull — Akizuki, theorem of      77
Kummer extension      278 380
Kummer theory      277 279 340
Kummer, E.      16 38
Kurschak J.      107
L-function of a $G(\mathbb{C|K})$ -set      455
L-series, Artin and Hecke L-series      539
L-series, Artin L-series      518
L-series, completed Artin L-series      537
L-series, completed Dirichlet L-series      437
L-series, completed Hecke L-series      499 503
L-series, Dirichlet L-series      435 496
L-series, functional equation      440 502 540
L-series, Hecke L-series      493 496
L-series, p-adic L-series      516
L-series, partial L-series      496
Langlands Philosophy      549
Lattice      2 23
Lattice, $\mathbb{Z}$ -structure      24
Lattice, basis of      24
Lattice, complete lattice      24
Lattice, fundamental mesh      24
Lattice, Minkowski's lattice point theorem      27
Lattice, unit lattice      40
Lattice, volume of fundamental mesh      26
Legendre symbol      50 336
Legendre's duplication formula      421 456
Lemma (renowned lemmas), Hensel's lemma      129
Lemma (renowned lemmas), Krasner's lemma      152
Lemma (renowned lemmas), Nakayama's lemma      72
Lemma (renowned lemmas), snake lemma      79
Length of a module      82
Leopoldt Conjecture      394
Lichtenbaum conjecture      516
Limit, inductive (direct)      266
Limit, projective      103 266
Line bundle      208 255
Local class field      322
Local class field, axiom      317
Local class field, theory      317
Local field      134
Local field, 2-local field      310
Local norm residue symbol      321
Local reciprocity law      320
Local ring      66
Local-to-global principle      161 357 384 385 391
localization      65 71
Localization of a valued field      160
Logarithm higher-dimensional      445
Logarithm of a formal group      343 345
Logarithm p-adic      136 142
Lubin — Tate, extension      348
Lubin — Tate, module      343
Lubin — Tate, series      328
Mackey functor      307
Maximal order      72
Maximal tamely ramified extension      157
Maximal unramified extension      154 285
Maximal unramified extension of $\mathbb{F}_{p}((t))$       176
Maximal unramified extension of $\mathbb{Q}_{p}$       176
Measure, canonical on $\mathbb{R}$       446
Measure, canonical on $\mathbb{R}_{+}^{*}$       454
Measure, canonical on Minkowski space      29
Measure, Haar measure on $\mathbf{R}$       446
Measure, Haar measure on a p-adic number field      142
Measure, Minkowski measure      221
Mellin principle      423
Mellin transform      422
Metric, canonical on Minkowski space      29
Metric, Hermitian      226
Metric, Minkowski      31
Metric, standard      28 228
Metric, trivial      227 229
Metrized, $\mathcal{O}$ -module      227
Metrized, number field      222
Metrized, projective resolution      234
Microprime      290 299
Minkowski — Hasse, theorem of      385
Minkowski, H.      24
Minkowski, H., bound      34
Minkowski, H., lattice point theorem      27
Minkowski, H., measure      221
Minkowski, H., metric      31
Minkowski, H., space      29 444
Minkowski, H., theorem on discriminant      38 207
Minkowski, H., theorem on linearforms      28
Minkowski, H., theory      28
Minkowski, H., theory, multiplicative version      32
Modular form      434
Modular function      402
Modulation      307
Module $\mathfrak{m}$       363
Module $\mathfrak{m}$ of a Hecke character      480
Module of definition      407
Moebius function      474
Moebius inversion formula      484
Monogenous ring extension      178
Mordell conjecture      207
Multiplicity of a representation      519
n-th ramification group      176
Nakayama's lemma      72
Nart, E.      149

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