Silverman J.H. — The arithmetic of elliptic curves :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Silverman J.H. — The arithmetic of elliptic curves

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: The arithmetic of elliptic curves

Автор: Silverman J.H.

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 402

Добавлена в каталог: 12.03.2005

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

Предметный указатель

m-torsion subgroup (E[m]), reduction map injects      176 179 193 196 222 282 298 310
Mahler, K.      244
Manin, Ju.      223 355
MAP      see also Isogeny; Morphism; Rational Map
Map between curves      23—30 41 43
Map between varieties      15—18
Map constant      25
Map of degree one      25 53 64 105 290
Map, analytic      159 161
Map, continuous      187 334
Map, defined over K      15
Map, degree      25 42 76 246
Map, finite      25 75
Map, inseparable      25 70
Map, multiplication      see Multiplication-by-m map
Map, ramification index      28 41 76 246
Map, separable      25 34 35 41 43 70 76 78 83
Map, translation      68 75 76 80
Map, unramified      28 76 79 107 251 252
Mass formula      145
Masser, D.      263
Maximal abelian extension      188 236
Maximal abelian extension of $\mathbb{Q}(\mathbb{Q}^{ab})$       338 341
Maximal abelian extension of a quadratic imaginary field      341 342
Maximal abelian extension, everywhere unramified      167 339 340 341
Maximal abelian extension, unramified outside S      194 196
Maximal real subfield      354
Maximal unramified extension of a local field $(K^{nr})$       178 185
Mazur, B.      223 265 355
Mean value theorem      243 260
Measure      231 272
Mellin transform      361 362
Mestre, J.-F.      234
Minimal discriminant      see Discriminant
Minimal field of definition      10 191 213
Minimal polynomial      243
Minimal scheme      358
Minimal Weierstrass equation      see Weierstrass equation
Minkowski, H.      196 231 232
Modular curve      223 338 351—355
Modular curve, affine      354
Modular curve, cusps      354
Modular curve, genus      351 355
Modular form      344 345
Modular form for a congruence subgroup      350 351
Modular form, algebra of      347 348
Modular form, associated L-series      360—362
Modular form, Fourier series      344 345 348
Modular form, product expansion for $\Delta$       345
Modular function      3 147 161 338 339 342—351 355
Modular function for a congruence subgroup      350
Modular function, field of      347 348
Modular function, Fourier coefficients      345
Modular function, Fourier series      344 345 355
Modular function, weight of      344
Modular group $(SL_2(\mathbb{Z}))$       343 344 346 349—354 362
Moduli space      352 353
Modulus of an elliptic integral      168
Mordell conjecture      94 266
Mordell — Weil group      189 233 267
Mordell — Weil group over an infinite extension      236
Mordell — Weil group, computation of      276—323
Mordell — Weil group, computation of, via two-isogeny      302
Mordell — Weil group, computation of, via [2]-descent      281
Mordell — Weil group, computation of, via [m]-descent      305
Mordell — Weil group, examples      275 282 303 311 314 315
Mordell — Weil group, height of generators      235 263 269 305
Mordell — Weil group, rank of      see Rank of an elliptic curve
Mordell — Weil group, torsion subgroup      see Torsion subgroup
Mordell — Weil theorem      60 189 197 199 205 215 220 231 233 241 367;
Mordell — Weil theorem over $\mathbb{Q}$       201—205
Mordell — Weil theorem, lack of effectivity      196 201 263 269 276 279 304
Mordell, L.J.      266 316 348
Morphism      16 19 68 288;
Morphism between curves      23 24 26
Morphism between projective spaces      17 208 217
Morphism, defined by a rational function      24 33 215 286
Multiplication-by-w map ([m])      45 57 71 73 91 197 254 301 304
Multiplication-by-w map ([m]) in characteristic p      137
Multiplication-by-w map ([m]) is finite      71
Multiplication-by-w map ([m]) is separable      83
Multiplication-by-w map ([m]) is unramified      251 252
Multiplication-by-w map ([m]) on a formal group      116
Multiplication-by-w map ([m]), degree of      86 89 105 106 107 163
Multiplication-by-w map ([m]), dual of      86
Multiplication-by-w map ([m]), effect on height      219 229 239
Multiplication-by-w map ([m]), kernel of      see m-torsion subgroup
Multiplicative reduction      see Reduction of an elliptic curve
Nagell, T.      221
Negation formula      58
Neron model      184 357—359 361
Neron — Ogg — Shafarevich criterion      179 184 322 340
Neron — Tate height      see Height canonical
Neron — Tate pairing (<,>)      229 232;
Neron, A.      183 184 227 229 234 358 364 367
Nevanlinna theory      268
Newton iteration      112
Node      48 50 60 61 104 180 240 357
Noether      321
Noetherian      42
Non-Abelian cohomology      335—336
Non-commutative formal group      129
Non-singular curve      21 25 26
Non-singular hypersurface      20
Non-singular part of $E(E_{ns})$       60—63 104 173 174 176 180 183
Non-singular point      8 9 14 20
Non-singular reduction      see Reduction of an elliptic curve good
Non-singular variety      8 133
Non-singular Weierstrass equation      50 63 64
Non-split reduction      see Reduction of an elliptic curve
Non-vanishing differential      36 52 159
Norm      101 257 258 274
Nullstellensatz      209 211 239
Number of points of bounded height      205 214 236
Number of points over finite fields      130—132 360
Number of points, integral points      250 251 272
Odd function      155 219;
Ogg's formula      361
Ogg, A.      184 361
One-coboundary      331
One-cochain      331
One-cocycle      20 190 197 236 258 331
One-cocycle, continuous      334
One-unit      118
Order in a field or algebra      100 102 108 137 145 164 165
Order of a differential      36
Order of a function       22 32 249
Order of a meromorphic function at a point       151
Order of an elliptic function      151 152
Order, associated to a valuation       189 195 255 280 361
Ordinary      137 144;
Orthogonal basis      274
p-torsion in characteristic p      64 137
parabola      1
Parallelogram law      229
Parallelogram law $\Rightarrow$ quadratic      230
Parametrized by modular functions      see Weil curve
Parshin, A.N.      266
Perfect field      5
Period of a homogeneous space      321—322 362
Periods of an elliptic curve      149 162 168
Periods of an elliptic curve are independent      149 161
Picard group (Pic)      32 33 34 42 66 75 84
Picard group (Pic) of a homogeneous space      295 321
Picard group (Pic), K-rational subgroup       32 33 44
Picard — Fuchs differential operator      143
Pigeon-hole principle      242 270
Point of finite order      see Torsion point
Point(s) at infinity      14 22 26 33 46 50 55 62 132 293 349
Pointed set      285 336

Pole      22 24 38 64 151 152 154 155 157 246 249
Positive definite quadratic form      88 131 231 232 274
Positive divisor      see Divisor
Potential good reduction      see Reduction of an elliptic curve
Principal divisor      32 67
Principal divisor has degree zero      32
Principal homogeneous space      see Homogeneous space
Principal ideal domain      194 205 206 227 255 267 275
Product formula      207 271
Profinite group      333
Profinite topology      333 334 336
Projective algebraic set      11
Projective closure      13 26 293
Projective space      10 20
Projective variety      12 13 132—134
Purely inseparable map      25 30 70 137;
q-expansion      see Fourier series
Quadratic character      132 141 287
Quadratic form      88 131 219 227 231 232 233 239 274
Quadratic imaginary field      100 102 145 164 167 339—342
Quadratic imaginary field, abelian extension      339—342
Quadratic imaginary field, class field theory      339—342
Quadratic imaginary field, class number one      340
Quadratic imaginary field, order in      108 137 164 165
Quadratic real field      235
Quadratic reciprocity      2 317
Quadric surface      106
Quantitative estimate      235 250 254
Quartic residue      316 318
Quasi-minimal Weierstrass equation      238 251
Quasi-parallelogram law      365
Quasi-period      166 346 365
Quaternion algebra      100 102 108 137
Quaternion algebra, maximal order      108
Quaternion algebra, ramified      102
Quaternion algebra, split      102 108
Quaternion group      329
Quotient of a curve by a finite group      78 107 341
Ramanujan $\tau$ -function      345 348
Ramanujan, S.      345
Ramification index      28 41 76 246
Ramified quaternion algebra      102
Rank of an elliptic curve      189 233—235 255 362 363
Rank of an elliptic curve of a twist      323
Rank of an elliptic curve over an infinite extension      236
Rank of an elliptic curve, can be arbitrarily large?      234
Rank of an elliptic curve, examples with large rank      234 367
Rank of an elliptic curve, one      275 314 363
Rank of an elliptic curve, relation with integral points      251
Rank of an elliptic curve, upper bound for      235 277 311 323
Rank of an elliptic curve, zero      314 316
Rational map      15 16 19;
Rational map of smooth curves is a morphism      23 26 64 68
Rational map, defined at a point      16
Rational map, defined by a function      24 33 215
Rational map, defined over K      15
Rational map, need not be a morphism      17 237
Rational map, regular      16 23
Rational map, value at a point      16
Rational point group      305
Reduction map      173 176 194 358
Reduction map is injective on torsion      176 179 193 194 298
Reduction map, kernel of      174 194 357 358
Reduction modulo $\pi$       171 173 174
Reduction of an elliptic curve $(\tilde{E})$       60 173 179—183 193 240 357
Reduction of an elliptic curve $(\tilde{E})$ at $v(\tilde{E}_v)$       193 360
Reduction of an elliptic curve $(\tilde{E})$ , additive (unstable)      180 181 186 359—361
Reduction of an elliptic curve $(\tilde{E})$ , bad      179—181 192 193 198 240 278 281 299 357 360
Reduction of an elliptic curve $(\tilde{E})$ , change under field extension      181
Reduction of an elliptic curve $(\tilde{E})$ , everywhere good      238
Reduction of an elliptic curve $(\tilde{E})$ , good (stable)      179—181 184—188 192 238 263 266 273 322 328 341
Reduction of an elliptic curve $(\tilde{E})$ , good (stable), $\Rightarrow$ injective on torsion      176 179 193 196 222 282 298 310
Reduction of an elliptic curve $(\tilde{E})$ , good (stable), finitely many with, outside S      263
Reduction of an elliptic curve $(\tilde{E})$ , good (stable), for all but finitely many v      193
Reduction of an elliptic curve $(\tilde{E})$ , isogenous curves      185
Reduction of an elliptic curve $(\tilde{E})$ , multiplicative (semi-stable)      180 181 186 328 357 359—361
Reduction of an elliptic curve $(\tilde{E})$ , non-singular part $(\tilde{E}_{ns})$       173 174 176 180 183 358 360
Reduction of an elliptic curve $(\tilde{E})$ , non-split      180
Reduction of an elliptic curve $(\tilde{E})$ , none over Q      239 264
Reduction of an elliptic curve $(\tilde{E})$ , potential good      181 186 187
Reduction of an elliptic curve $(\tilde{E})$ , split multiplicative      180 183 328 357 359 360 366
Regular differential      see Holomorphic differential
Regular function      9 15 22 35
Regular homomorphism      258
Regular of a number field      232 269
Regular rational map      23
Regular scheme      357 358
Regulator elliptic      233 234 362
Reichardt, H.      304
Relative Selmer group      305
Representation      90 92 134;
Residue of a differential      137
Residue of a function      151 152 154
Residue theorem      151
Restriction map on cohomology      297 320 332 334 337
Restriction map on cohomology, image of      337
Restriction map on cohomology, kernel of      337
Resultant      204
Riemann hypothesis      134 136 137
Riemann surface      146 148 149 158
Riemann zeta function      166 236 338
Riemann — Roch theorem      37 39 40 42 45 57 63—66
Riemann — Roch theorem, effective version      261
Rohrlich, D.      371
Roots of unity      91 95 98 194 258 277 338
Roth's lemma      270
Roth's theorem      3 244 254 269—272
Roth, K.F.      244
S-integers      194 227 241 248 251
S-integral points      see Integral points
S-minimal Weierstrass equation      227
S-regulator homomorphism      258
S-unit equation      241 252—256 257 262 269
S-unit equation, effective bound      259
S-unit equation, number of solutions      254
S-unit group      194 241 249 261
S-unit theorem      195 253 255 258
Scalar multiplication      159 160 163
Schanuel, S.      214
Scheme      357—360
Schmidt, F.K.      370
Schmidt, W.      244 268
Schneider, T.      256 257
Schur's lemma      341
Secant line      14
Segre embedding      236
Selmer conjecture      315
Selmer group      296—306 311 316;
Selmer group is effectively computable      299
Selmer group is finite      298
Selmer group, examples      300 303 311 323
Selmer group, relative      305
Selmer, E.      12 304
Semi-stable reduction theorem      181 328
Separable degree      25 42 70 76
Separable extension      22 35 44 329
Separable map      25 34 35 41 43 70 76 78 85
Serre, J.-P.      144 184 265 366 370 371
Shafarevich — Tate group      276 296—306 311 315 316 322 362 363;
Shafarevich — Tate group is finite?      277 305
Shafarevich — Tate group, Cassels pairing      306 315 364
Shafarevich — Tate group, examples      300 303 311 314
Shafarevich — Tate group, non-trivial elements      316
Shafarevich's theorem      263—266
Shafarevich, I.R.      184 234 263 266 371
Sheaf cohomology      137
Shimura, G.      361 362
Siegel's identity      256
Siegel's theorem      60 241 247 252 254 264 265 266 273
Siegel's theorem is not effective      250

1 2 3 4

О проекте