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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Natural density      543
Newton polygon      144
Noether, E.      282
Nonarchimedean valuation      118
Norm      8
Norm of a gaussian integer      2
Norm of an ideal      186
Norm of anidele      370
Norm on C      444
Norm residue group      277
Norm residue symbol      302
Norm residue symbol, global      391
Norm residue symbol, local      321
Norm residue symbol, over $\mathbb{Q}_p$       331
Norm residue symbol, product formula      393
Norm theorem, of Hasse      384
Norm topology      303
Norm, absolute      34 184 186 361
Norm, Coleman's norm operator      351
Norm, Hasse norm theorem      384
Norm, universal norms      304 308
Norm-one surface      39 460
Normalization      7 76 91
Normalized valuation      121 184
Number field, $\mathfrak{p}$ -adic      136
Number field, algebraic      5
Number field, discriminant of      15
Number field, genus of      214 467
Number field, imaginary quadratic      402
Number field, metrized      222
Number field, quadratic      50
Numbers, $\mathfrak{p}$ -adic      128 136
Numbers, algebraic      5
Numbers, Bernoulli      38 427 441 515
Numbers, Fibonacci      53
Numbers, ideal      16 486
Numbers, p-adic      100 101 111
Odlyzko, A.M.      223
Order of a number field      72
Order of a number field, maximal      72
Ostrowski, theorem of      124
p-adic absolute value      107
p-adic expansion      99 101 114
p-adic exponential valuation      107
p-adic L-series      516
p-adic numbers      100 101 111 271
p-adic unit rank      394
p-adic units      112
p-adic valuation      69
p-adic Weierstrass preparation theorem      116
p-adic zeta function      516
p-adic, periodic p-adic expansion      106
p-class field theory      298 326 332
p-Sylow subgroup      274
Partial, Hecke theta series      489
Partial, L-series      496
Partial, zeta function      458
Pell's equation      43 84
Periodic p-adic expansion      106
Picard group      75 185
Picard group, replete      186 239
Place      183
Poincare homomorphism      234 237
Poisson summation formula      447
Polyhedric cone      504
Pontryagin dual      273
Power residue symbol      336 415
Power series field      127 136
Power sum      433 443
Preparation theorem (Weierstrass)      116
Presheaf      87
Prime (place), absolute norm of      184
Prime (place), complex      183
Prime (place), finite      183
Prime (place), infinite      183
Prime (place), microprime      290 299
Prime (place), real      183
Prime decomposition      18 409
Prime decomposition in the cyclotomic field      61
Prime decomposition of gaussian integers      1
Prime element      121 289
Prime number theorem, of Dirichlet      64 469 543
Primitive character      434 472
Primitive polynomial      129
Primitive root of unity      59
Principal character      435 520
Principal divisor      83
Principal divisor, replete      189
Principal ideal theorem      410
Principal ideal, replete      186
Principal idele      359
Principal units      122
Procyclic groups      273
Product formula for absolute values      108 109 185
Product formula for the Hilbert symbol      414
Product formula for the norm residue symbol      393
Product, restricted      357
Profinite completion      274
Profinite group      264
Projection formula      248
Projective, $\mathcal{O}$ -module      228
Projective, limit      103 266
Projective, line      97
Projective, resolution      234
Projective, system      266
Prufer ring $\hat{\mathbb{Z}}$       272
Purely ramified      49 158 286
Pythagorean triples      5
Quadratic number field      50
Quadratic residue      50
Quadratic residue symbol      50 417
Ramification field      175
Ramification group      168
Ramification group, Herbrand's theorem      180
Ramification group, higher      176 352
Ramification group, upper numbering of      180
Ramification index of metrized number fields      224
Ramification index of prime ideals      45
Ramification index of primes (places)      184
Ramification index of valuations      150 165
Ramification index, abstract      285 309
Ramification points      92
Ramification theory of valued fields      166
Ramification theory, higher      176 354
Ramification theory, Hilbert's      53
Ramified      49
Ramified covering      92
Ramified tamely      154
Ramified totally      49 158 286
Ramified wildly      158
Rank of coherent o-module      229 243
Rationally equivalent      83
Ray class field      366 396 403
Ray class group      363 365
Real prime      183
Reciprocity homomorphism      294
Reciprocity law for power residues      415
Reciprocity law, Artin reciprocity law      390 407
Reciprocity law, Gauss's reciprocity law      51 416
Reciprocity law, general      300
Reciprocity law, global reciprocity law      390
Reciprocity law, local reciprocity law      320
Reciprocity map      291
Reciprocity, Frobenius      521
Regular prime ideal      79
Regular prime number      38
Regular representation      520
Regulator      43 431 443
Replete ideal      185
Replete ideal class group      186

Replete ideal, absolute norm of      186
Replete ideal, degree of      213
Replete ideal, replete principal ideal      186
Replete ideal, volume of fundamental mesh      212
Replete, divisor      189
Replete, divisor class group      190
Replete, Grothendieck group      233
Replete, Picard group      186
Replete, principal divisor      189
Replete, principal ideal      186
Representation of a group      518
Representation of a group, augmentation representation      520
Representation of a group, character of      519
Representation of a group, degree      519
Representation of a group, equivalent representations      519
Representation of a group, induced      521
Representation of a group, irreducible      519
Representation of a group, multiplicity of      519
Representation of a group, regular      520
Residue class field      121
Residue of a $\mathfrak{p}$ -adic differential      341
Residue of L-series      423
Residue of zeta functions      425
Restricted product      357
Ribet, K.      38
Riemann — Hurwitz formula      220 221 224
Riemann — Roch, for number fields      213 214 218
Riemann — Roch, Grothendieck — Riemann — Roch for number fields      254
Riemann — Roch, theorem of      209
Riemann's zeta function      419
Riemann's zeta function, completed      422 466
Riemann's zeta function, Euler's identity      419 435
Riemann's zeta function, functional equation      425 426
Riemann's zeta function, special values of      427 431 432
Riemann's zeta function, trivial zeroes      432
Riemann, B., hypothesis      432
Riemann, B., surface      208
Ring of adeles      357
Ring of p-adic integers      104 111 271
Ring of Witt vectors      134 283
Ring, Dedekind domain      18
Ring, factorial      7
Ring, henselian      152.
Ring, henselian valuation ring      143
Ring, local ring      66
Ring, Prufer ring $\hat{\mathbb{Z}}$       272
Ring, valuation ring      121
Row-column expansion      6
S-class group      71
S-idele      358
S-units      71 358
Safarevic conjecture      207
Safarevic, I.R.      413
Scheme      88 96
Schmidt, F.K.      58 152
Schwartz function      446
Section of a sheaf      87
Serre duality      209 214
Sesquilinear      226
Sheaf      88
Sheaf, presheaf      87
Sheaf, section of      87
Sheaf, stalk of      88
Sheaf, structure sheaf      88
Shintani's unit theorem      507
Siegel — Klingen, theorem of      515
Simplicial cone      504
Singularity      73 91
Singularity, resolution of singularities      91
Snake lemma      79
Solenoid      368
Spectrum of a ring      85
Stalk of a sheaf      88
Standard metric      28 228
Stickelberger's discriminant relation      15
Stirling's formula      206
Strict cohomological dimension      306
Strong approximation theorem      193
Structure sheaf      88
Supplementary theorems      340 416
Sylow subgroup      274
Symbols, Artin symbol      407
Symbols, Hilbert symbol      305 333
Symbols, Jacobi symbol      417
Symbols, Legendre symbol      50 336
Symbols, norm residue symbol      302 321 331 391 393
Symbols, power residue symbol      336 415
Symbols, quadratic residue symbol      417
Symbols, tame Hilbert symbol      335
Symbols, [x, a)      341
Takagi, T.      406
Tamagawa measure      432
Tame Hilbert symbol      335
Tamely ramified      154
Tamely ramified, maximal extension      157
Tamely ramified, maximal extension of $\mathbb{F}_{p}((t))$       176
Tamely ramified, maximal extension of $\mathbb{Q}_p$       176
Tamme, G.      225 240
Taniyama — Shimura — Weil conjecture      38
Tate duality      326 404
Tate's thesis      503
Tautological class field theory      306
Taylor, R.      38
Theorem (renowned theorems) Artin — Hasse      339
Theorem (renowned theorems) Brauer      522
Theorem (renowned theorems) Bruckner      339
Theorem (renowned theorems) Cebotarev      545
Theorem (renowned theorems) Dwork      332
Theorem (renowned theorems) Faltings (Mordell conjecture)      207
Theorem (renowned theorems) Fontaine      207
Theorem (renowned theorems) Grothendieck — Riemann — Roch      254
Theorem (renowned theorems) Grunwald      405
Theorem (renowned theorems) Hasse — Arf      355
Theorem (renowned theorems) Hasse — Minkowski      385
Theorem (renowned theorems) Herbrand      180
Theorem (renowned theorems) Hermite      206
Theorem (renowned theorems) Hilbert theorem 90      281
Theorem (renowned theorems) Hilbert — Noether      283
Theorem (renowned theorems) Kronecker- Weber      324 398
Theorem (renowned theorems) Krull — Akizuki      77
Theorem (renowned theorems) Minkowski lattice point theorem      27
Theorem (renowned theorems) Minkowski theorem on the discriminant      207
Theorem (renowned theorems) Minkowski — Hasse      385
Theorem (renowned theorems) Ostrowski      124
Theorem (renowned theorems) Riemann — Roch      209 218
Theorem (renowned theorems) Riemann — Roch — Grothendieck      254
Theorem (renowned theorems) Schmidt, F.K. (henselian valuation)      152
Theorem (renowned theorems) Schmidt, F.K. (prime decomposition)      58
Theorem (renowned theorems) Siegel — Klingen      515
Theorem (renowned theorems) Wilson      2
Theorem (renowned theorems), Artin reciprocity law      390
Theorem (renowned theorems), Dirichlet density theorem      543
Theorem (renowned theorems), Dirichlet prime number theorem      469
Theorem (renowned theorems), Dirichlet unit theorem      42 81 358
Theorem (renowned theorems), extension theorem (for valuations)      161 163
Theorem (renowned theorems), Gauss reciprocity law      51 64 416
Theorem (renowned theorems), Hasse norm theorem      384
Theorem (renowned theorems), principal ideal theorem      410
Theorem (renowned theorems), Shintani unit theorem      507
Theorem (renowned theorems), Weierstrass preparation theorem      116
Theta series      443
Theta series of a lattice      450
Theta series of an algebraic number field      484
Theta series, Hecke      489
Theta series, Jacobi      422 424
Theta series. transformation formula      425 437 438 439 452 490
Todd class      254
Topology, Etale      90
Topology, Krull      167 262
Topology, norm      303

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