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| Ïîèñê ïî óêàçàòåëÿì |
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| Lang S. — Diophantine Geometry |
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| Ïðåäìåòíûé óêàçàòåëü |
Logarithmic discriminant 55 146
Logarithmic discriminant, height 43
Lower bound conjectures 74 100 243
Lu — Yau 180
Maehara 24
Mahler 58 217 220
Manin — Mumford conjecture 37 38
Manin — Zarhin equations for abelian varieties 26 77
Manin — Zarhin equations for abelian varieties, height with canonical coordinates 77
Manin, Brauer group 253
Manin, constant 140 141
Manin, counting 260—262
Manin, cubic surfaces 23 48
Manin, elliptic curves 253
Manin, function field case of Mordell 13 37 153—161
Manin, letter 158
Manin, obstruction 250 253—258
Manin, unirationality 23
Mason theorem 48 65
Mason theorem in several variables 66
Masser lower bound on height 74 240 243
Masser — Oesterle abc conjecture 48
Masser — Wustholz theorem 121 238—239
Masser — Wustholz theorem, replacement of Raynaud theory 122
May’s theorem 58
Mazur, Eisenstein quotient 129
Mazur, points in cyclotomic extensions 29
Mazur, torsion group 28 127—130 134
Measure hyperbolic 186
Mestre 28 170
Metrized vector sheaf 167
Minimal discriminant 73 97 134
Minimal height 73 74
Minimal height conjecture 100
Minimal model 97
Minimal Neron differential 140
Miranda — Persson on torsion 27
Miyaoka 151
Miyaoka — Mori 20
Modular elliptic curve 132 136 138—142
Modular representation 133 134
Modular units 37 141
Moduli space 118 119
Mordell conjecture 12 106
Mordell conjecture, Faltings proof 107—121
Mordell conjecture, function field case 13 143—162
Mordell conjecture, Vojta’s proof 230
Mordell objection to Riemann — Roch 230
Mordell — Weil, group and units 142
Mordell — Weil, in abelian extensions 29
Mordell — Weil, Shioda lattice 75
Mordell — Weil, theorem 26 27 “Specialization” “Torsion
Mordellic 15 16 25 36 179
Moret — Bailly 170
Mori — Mukai 20
Mori, on Hartshorne conjecture 20
Mori, proof of Ueno’s theorem 35
Mori, theorems on rational curves 19 20
Multiplicative height 54
Mumford 20 23 26 61 62
Mumford, equations for abelian varieties 26
Mumford, gaps between heights of points 61 62
Narasimhan — Nori theorem 103
Neron — Severi group 30 32—34 77 79 149 261
Neron — Tate height 72—75 82 85 86 241 242
Neron — Tate height and Weil height 72
Neron — Tate height, estimates by Demjanenko 72
Neron — Tate height, estimates by Zimmer 72
Neron — Tate norm 73
Neron — Tate norm, quadratic form 72—75
Neron, algebraic families of Neron functions 213
Neron, function 210 212
Neron, model 19 69—71 79—82 94 95 115—117 120
Neron, pairing 212
Neron, rank 41 42
Neron, specialization theorem 41
Neron, symbol 212
Neron, theorem on Mordell — Weil 26
Nevanlinna theory 192—204
Nevanlinna theory for coverings 204
Newton approximation 249 259
Noether and Galois groups 42
Noether’s formula 152 168
Noguchi 36 183 184 190—192
Non-degenerate 202
Non-singular 4
Non-singular Hasse principle 248—258
Non-singular rational point as birational invariant 249
Norm as height 73 85 86 236 241 242
Norm form 245
Normal crossings 191
Normalized differential of first kind 136
Normalized theta function 209
Northcott theorem 56
Number field 12
Ochiai on Bloch conjecture 182
Ochiai on Bloch conjecture on Ueno — Kawamata fibrations 36 (see also “Kobayashi — Ochiai”)
Ogg on bad reduction 71 98
One-parameter subgroup 183
Order at p 44
Order of a function at a divisor 6
Order of the conductor 71
Ordinary abelian variety 161 162
Ordinary absolute value 44
Osgood 216 221
p-adic absolute value 44
Parshin — Arakelov proof of Shafarevich conjecture in function field case 104
Parshin, construction 104 105 170
Parshin, hyperbolic method 149 187—189
Parshin, inequality 170
Parshin, integral points in function field case 189 221
Parshin, method with canonical sheaf 149
Parshin, proof of Raynaud theorem in function field case 189
Parshin, Shafarevich implies Mordell 104 105
Peck 248
Period 93 95 97 125 236 239
Period, lattice 125
Period, relations 239
Period, v-adic 93
Pfaffian divisor 148
Pic(X) 6 33 144
Picard group 6 33
Picard group, variety 33
Picard — Fuchs group 157 159
Poincare class 33
Polarization and polarized abelian variety 34 35 102 103 118 119 121 122 238 239
Polarization and polarized abelian variety, principal 102 103 119 121 “Lange” “Masser “Moduli “Torelli”)
Polarization and polarized abelian variety,v degree 35 103 121 122 238 239
Polynomial equations 3
Positive (1, l)-form 185
Positive cone in Neron-Severi group 261
Positivity of canonical sheaf 170
Positivity of Weil functions 208
Power series 247
Principal homogeneous spaces 85—91 256
Principal polarization 102 103 118 119 121
Product formula 45 52
Projective bundle 147
Projective bundle, variety 2
Proper set of absolute values 53 58
Properties of height in Nevanlinna theory 194—196
Properties of height in number theory 58—61
Proximity function 193 211
Pseudo ample 9 19 67 181 198 244 258
Pseudo ample, anti-canonical class 244 257 258
Pseudo ample, canonical class 15 35 67 179 180 198
Pseudo ample, Kodaira condition 9
Pseudo canonical variety 15 17 35 36 179—181
Pseudo hyperbolic 180—181
Pseudo Mordellic 17 180—181
| Pseudofication 15 179—181
Pythagorean triples 135
Quadratic form see “Neron — Tate”
Quadratic forms in 9 variables 249
Quasi function 207
Quasi-algebraic closure 245—248 259
Quasi-projective variety 3
Quintic threefold 21 34
Ramanujan’s taxicab point 23
Ramification, counting function 197 199 201—204
Ramification, divisor 196 202
Ramification, order 196 105
Rank, average 28
Rank, cyclotomic extensions 29
Rank, Demjanenko — Manin criterion 79
Rank, elliptic curve 28 42 92 139—142
Rank, finitely generated group 240—243
Rank, generic case 27
Rank, high rank by Neron specialization 42
Rank, Mestre 28
Rank, Mordell — Weil group 28 92 139—142 237
Rank, Neron — Severi group 261
Rank, rank 1 over the rationals 138—141 (see also “Birch — Swinnerton — Dyer” “Brumer “Neron” “Shafarevich “Zagier
Rational curves 16 18—20 22 23 244 260 247
Rational differential form 10
Rational function 4
Rational group variety 16
Rational map 5
Rational point 2
Rational point on Chatelet surface 257
Rational points in completions 249
Rational variety 6 16 20 250 256
Rationally equivalent 6 7
Raynaud, bad reduction 71
Raynaud, conductor 71
Raynaud, division points 37 38 170
Raynaud, Faltings height 119
Raynaud, formula for the degree of the Lie sheaf 120
Raynaud, function field case 39
Raynaud, Parshin’s proof 189
Raynaud, theorems 37
Raynaud, torsion and division points 37 38 170
Reduction homomorphism 84
Reduction homomorphism and Voloch theorem 162
Reduction modulo a prime ideal 68
Regular differential form 14
Regulator 55 93 98
Regulator of Mordell — Weil group 93 98
Relations 242
Relative canonical class 146
Relative case 12
Relative cohomology group 154
Relative Gauss — Manin connection 155
Relative tangent sheaf 173
Relatively algebraically closed 258
Representation, finite at a prime 134 (see also “Galois representation” “l-adic
Residue class field 3
Restriction of scalars 245
Ribet, Galois representations for Fermat 132
Ribet, theorem on Fermat 134
Ribet, torsion group in cyclotomic fields 29
Ricci form 185 202
Richtmayer — Devaney — Metropolis 214
Riemann form 209
Riemann — Roch 173—175 214 230 232 233
Riemann — Roch in Roth theorem 214
Riemann — Roch in Vojta’s proof 230
Riemann — Roch, objection by Mordell 230 (see also “Bombieri” “Gillet
Robba 259
Rosenlicht 106
Roth theorem 215
Roth theorem, geometric version 218
Ru — Wong theorem 221
Rubin on Shafarevich — Tate group 89
S-integers 214
Saito, S. 71
Saito, T. 254
Salberger 249 255
Samuel proof in characteristic p 161
Sansuc 249—258
Sansuc, linear group varieties 256
Schanuel counting 262
Schanuel counting, theorem 58 260
Schinzel conjecture 257
Schmidt theorem 215 216 222 234
Schneider method 229
Second Main Theorem 196—204
Selmer, example 89
Selmer, group 88—91
Semiabelian variety 36 37 39
Semiabelian variety, Noguchi theorem 183
Semisimplicity of l-adic representations 107—111 113—115
Semisimplification 133
Semistable abelian variety 70 71
Semistable curve 150
Semistable reduction 70 71 117 120 121 149—151
Serre — Tate theorem 113
Serre, conjecture for Fermat 134
Serre, l-adic representations 134 135 237
Serre, local L-factors 92
Serre, semisimplicity 111 135
Serre, torsion points 39 111 237
Severi — Brauer 256
Shafarevich conjecture 104 106 111
Shafarevich conjecture, implied by Vojta conjecture 227
Shafarevich conjecture, implies Mordell 106
Shafarevich — Tate, exact sequence 88
Shafarevich — Tate, example of high rank in function field case 28 92
Shafarevich — Tate, group 88—91 94 96 98 99 139 140 253—255
Shatz 250 253
Shimura correspondence 141
Shimura on modular elliptic curves 132 136
Shimura on modular elliptic curves, on Taniyama 131
Shioda on generic torsion points 27
Shioda on generic torsion points on lattices from Mordell — Weil — Lang — Neron groups 75
Siegel 37 58 217 218 220 228 232
Siegel lemma 232
Siegel on integral points 217 218
Sign of functional equation 98 139
Silverberg on generic torsion points 27
Silverman theorem on heights in algebraic families 78 79
Silverman theorem on heights in algebraic families, conjecture on algebraic families of heights 81
Silverman — Tate theorem 77
Simple normal crossings 196 202 223
Siu 198
Soule 168 173—175 232
Sp (Special Set) questions 18 245
Special set 16 17—23 67 179 182 245
Special set and exceptional set 67
Special set, holomorphic 179
Special set, holomorphic and algebraic are equal 182
Special variety 17—20
Specialization map and homomorphism, on abelian varieties 41 42 78 79 84
Specialization map and homomorphism, on Brauer group 252
Specialization map and homomorphism, on sections 40
Specialization principle (local) 258 259
Split algebraic family 12 24 25 62 78 79 178 192
Stability 150
Stable Faltings height 117
Stably non-split and finiteness of rational points 187 188
Stably split 159 161
Stark 50 240
Stevens conjecture 141
Stoll on Nevanlinna theory 204
Strongly hyperbolic 185
Subvarieties of abelian varieties 20 21 35 36 181—183 220 232
Subvarieties of abelian varieties, Ax theorem 182
Subvarieties of abelian varieties, Faltings theorem 36 220
Subvarieties of abelian varieties, Green’s theorem 182
Subvarieties of abelian varieties, special set 36
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