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

$G^{ab}$ (maximal abelian quotient)      265 274
$v_{\mathfrak{p}}$ , for a prime $\mathfrak{p}$       184
$\hat{\mathbb{Z}}$       272
$\mathbb{Z}$ -structure      24
$\mathbb{Z}_p$ -extension, cyclotomic      326
$\mathfrak{p}$ -adic exponential function      137
$\mathfrak{p}$ -adic logarithm      136 142
$\mathfrak{p}$ -adic number field      136
$\mathfrak{p}$ -adic numbers      128 136 271
$\tilde{K}|K$ , maximal unramified extension      154 285
$\wp$ -function, of Weierstrass      401
Absolute Galois group      261
Absolute norm of a prime (place)      184
Absolute norm of a replete ideal      186
Absolute norm of an ideal      34
Absolute norm of an idele      361
Absolute value, p-adic      107
Absolute value, product formula      108 109 185
Abstract Galois theory      275
Abstract valuation theory      284
Adele      357
Admissible mono/epimorphism      231
Affine scheme      88
Algebraic number field      5
Algebraic numbers      5
Analytic class number formula      468
Approximation theorem      117
Approximation theorem, strong approximation theorem      193
Arakelov class group      190
Arakelov divisor      189
Archimedean valuation      118
Arithmetic algebraic geometry      193
Arithmetic progression      64 469 545
Artin conductor      527 533
Artin conductor, local Artin conductor      532
Artin conjecture      525
Artin L-series      518
Artin L-series, Artin and Hecke L-series      539
Artin L-series, completed Artin L-series      537
Artin L-series, functional equation      540 541
Artin L-series, zeroes of      541
Artin reciprocity law      390 407
Artin symbol      407
Artin — Hasse, theorem of      339
Artin — Schreier theory      281
Artin, E.      406 413
ASSOCIATED      3
Auberwesentliche Diskriminanten-teiler      207
Augmentation ideal, of a group ring      410
Augmentation ideal, of the Grothendieck ring      243
Augmentation representation      520
Basis, basis of a lattice      24
Basis, discriminant of a basis      11
Basis, integral basis      12
Battle of Hastings      44
Bauer, M., theorem of      548
Beilinson conjecture      432 443
Bernoulli numbers      38 427
Bernoulli numbers, generalized      441 515
Bernoulli polynomial      433 443 511
Big Hilbert class field      399
Bloch, S.      132
Borel, A.      132
Brauer, theorem of      322
Bruckner, H.      338 417
Bruckner, theorem of      339
Brumer, A      394
Canonical divisor      209
Canonical measure on $\mathbb{R}$       f46
Canonical measure on $\mathbb{R}_{+}^{*}$       454
Canonical measure on Minkowski space      129
Canonical metric      29
Canonical module of a metrized number field      222
Canonical module of a number field      219
Canonical module of a Riemann surface      209
Cebotarev density theorem      545
Central function      519
Centrally symmetric      26
Character, character group      273 280
Character, Chern character      244 246
Character, conductor of      434 473 478
Character, Dirichlet character      434 478
Character, exponent p of      435
Character, Grobencharacter      436 470
Character, Hecke character      480
Character, induced character      521
Character, irreducible character      520
Character, of a representation      519
Character, primitive Dirichlet character      434
Character, primitive Grobencharacter      472
Character, principal character      435 520
Character, trivial character      434
Characteristic polynomial of a field element      9
Characteristic, Euler — Minkowski      212 256 258
Characteristic, Euler — Poincare      209
Chern character      244 246
Chern class      244
Chevalley, C.      357
Chinese remainder theorem      21
Chow group      83 190
Chow theory      193
Class field      304
Class field axiom      299
Class field axiom, global class field axiom      383
Class field axiom, local class field axiom      317
Class field theory      300
Class field theory, existence theorem      322 396
Class field theory, global      357 390
Class field theory, higher-dimensional      310
Class field theory, local      317 320
Class field theory, p-class field theory      298 326 332
Class field theory, tautological      306
Class field, big Hilbert class field      399
Class field, global class field      395
Class field, Hilbert class field      399 402
Class field, local class field      322
Class field, problem of class field tower      413
Class field, ray class field      396
Class function      519
Class group      22
Class group, Arakelov class group      190
Class group, connected component of idele class group      368
Class group, divisor class group      83
Class group, ideal class group      22
Class group, idele class group      359
Class group, of an order      82
Class group, ray class group      363 365
Class group, replete divisor class group      190
Class group, replete ideal class group      186
Class group, S-class group      71
Class number      34 36 81
Class number formula      468
Class number, finiteness of      36 81
Closedness relation      108 185
Closure, integral      7
Coboundary      282
Cocycle      282
Cohomological dimension      306
Cohomology      284
Coleman's norm operator      351
Compact, $Pic(\overline{\mathcal{O}})^0$ is compact      193
Compact, compact group      269
Compactified Grothendieck group      233
Complementary module (Dedekind)      195
Complete lattice      24
Complete valued field      123 131
Completed L-series      437 499 503 537
Completed zeta function      422 466
Completed zeta function, functional equation      425 466
Completely split      49

Completion of a G -modulation      308
Completion of a valued field      123
Completion profinite completion      274
Complex multiplication      402
Complex prime      183
Conductor      47 79 323 397
Conductor, Artin conductor      527 532 533
Conductor, conductor-discriminant formula      534
Conductor, of a Dirichlet character      434 478
Conductor, of a Grobencharacter      473
Congruence subgroup      363
Conjectures, Artin conjecture      525
Conjectures, Beilinson conjecture      432 443
Conjectures, Fermat conjecture      37 38
Conjectures, Leopoldt conjecture      394
Conjectures, Lichtenbaum conjecture      516
Conjectures, Mordell conjecture      207
Conjectures, Riemann hypothesis      432
Conjectures, Safarevic conjecture      207
Conjectures, Taniyama — Shimura — Weil      38
Conjugate, embeddings      161
Conjugate, prime ideals      53
Conjugation on $\mathbb{C}$       444
Conjugation on $\mathbb{K_C}$       226
Connected component of the idele class group      368
Convex      26
Cotangent element      255
Covering      92 93
Covering transformation      93
Covering, ramified      92
Covering, universal      93
Critical strip      432
Crossed homomorphism      282
CYCLE      193
Cyclotomic field      58 158 273 398
Cyclotomic field, generalized cyclotomic fields      348
Cyclotomic field, prime factorization      61
Cyclotomic polynomial      59 166
Cyclotomic polynomial, generalized      348
Cyclotomic units      44
Cyclotomic, $\hat{{\mathbb{Z}}}$ -extension      385 386
Cyclotomic, $\mathbb{Z}_p$ -extension      326 386
Decomposition field of a microprime      290
Decomposition field of a prime ideal      54
Decomposition field of a valuation      171
Decomposition group of a microprime      290
Decomposition group of a prime ideal      54
Decomposition group of a valuation      167
Decomposition law      409
Decomposition law of prime numbers      61 409
Decomposition law of prime numbers in the cyclotomic field      61
Decomposition law of prime numbers in the ring of gaussian integers      4
Dedekind domain      18
Dedekind zeta function      457
Dedekind zeta function, functional equation      467
Dedekind's complementary module      195
Dedekind, R.      17
Degree map      190
Degree of a divisor      96
Degree of a replete divisor      190
Degree of a replete ideal      213
Degree of a representation      519
Degree valuation      95
Deninger, C.      542
Density theorem of Cebotarev      545
Density theorem of Dirichlet      543
Density, Dirichlet density      542
Density, natural density      543
Derivation      200
Determinant of a metrized $\mathcal{O}$ -module      231 245
Different      195 201 254
Different of a metrized number field      224
Different of an element      197
Differential module      200 254
Differentials      200 341
Diophantine equation      104
Direct (inductive) limit      266
Dirichlet character      434 478
Dirichlet density      542
Dirichlet L-series      435 496
Dirichlet L-series, completed      437
Dirichlet L-series, functional equation      440
Dirichlet L-series, special values of      442 443 515
Dirichlet L-series, zeroes of      442
Dirichlet, G.R. Lejeune      42
Dirichlet, G.R. Lejeune, density theorem      543
Dirichlet, G.R. Lejeune, prime number theorem      64 469 543
Dirichlet, G.R. Lejeune, unit theorem      42 81 358
Dirichlet-character, conductor of      434 478
Discrete subgroup ,      24
Discrete valuation      67 121
Discrete valuation of a function field      95
Discriminant      49 201 251
Discriminant and different      201
Discriminant of a basis      11
Discriminant of a number field      15
Discriminant of an element      11
Discriminant of an ideal      14
Discriminant, auberwesentliche Diskriminanten-teiler      207
Discriminant, bound      204 223
Discriminant, conductor-discriminant formula      534
Discriminant, Minkowski's theorem on      38 207
Discriminant, Stickelberger's relation      15
Distribution of prime:numbers      432
Division points of a formal group      347
Divisor      82
Divisor, Arakelov divisor      189
Divisor, Arakelov divisor class group      190
Divisor, canonical divisor      209
Divisor, Chow group      83
Divisor, degree of a divisor      96
Divisor, divisor class group      83
Divisor, divisor group      82 95
Divisor, group of replete divisor classes      190
Divisor, group of replete divisors      189
Divisor, principal divisor      83
Divisor, replete divisor      189
Divisor, replete principal divisor      189
Double cosets      55 58
Double functor      307
Dress, A.      307
Duality, dual ideal      194
Duality, Pontryagin dual      273
Duality, Serre duality      209
Duality, Tate duality      326 404
Duplication formula, Legendre's      421 456
Dwork, B.      298 332
Dwork, theorem of      332
Elliptic curve      402
Equidistributed prime; ideals      545
Equivalent representations      519
Equivalent valuations      116
Etale topology      90 93
Euler factors at infinity      459 527 535 541
Euler product      419 435
Euler — Minkowski characteristic      212 256 258
Euler — Poincare characteristic      209
Euler's identity      419 435
Euler, L.      64 431
Existence theorem of class field theory      322 396
Expansion, p-adic expansion      99 101 106
Expansion, row-column expansion      6
Exponent of a Grobencharacter      478
Exponent of an operator p      278
Exponent, exponent p of an character      435
Exponential function, p-adic      137
Exponential valuation      69 107 120 184
Extension of a valuation      161 163
Extension of a valuation of a complete field      131
Extension of a valuation of a henselian field      144 147

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