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| Ïîèñê ïî óêàçàòåëÿì |
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| Lang S. — Diophantine Geometry |
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| Ïðåäìåòíûé óêàçàòåëü |
Fermat, fibrations 23
Fermat, Frey elliptic curve 132 135
Fermat, hypersurface 22 23
Fermat, modular curve correspondence 23 225
Fermat, Ribet’s reduction of last theorem to Taniyama — Shimura 132
Fermat, Taniyama — Shimura implies Fermat 132
Fermat, theorem for polynomials 48
Fermat, unirational for low degree? 22 23
Fermat, Vojta’s conjecture implies Fermat asymptotic 64
Fibration 18 20—24 35 36 183 256 257
Fibration by conies 253 255 256 257
Fibration of Chatelet surface 256 257
Fibration of Fermat 23
Fibration of generic quintic threefold 21
Fibration of K3 surface 20
Fibration of Kummer surface 20
Fibration of subvarieties of abelian varieties 35 36 183
Finite representation at a prime 134
Finitely generated extensions 12 15 16 27 33 42 111 112
Finitely generated extensions, group 26—32 36—40 240—243
Finiteness I 106
Finiteness II 107
Finiteness, Brauer group 254
Finiteness, Chow group generators 34
Finiteness, curves with good reduction 104
Finiteness, Faltings heights 120
Finiteness, integral points 50 217 221
Finiteness, isogenies 106—109 115 120 121 122 128 238 239
Finiteness, isomorphism classes of abelian varieties 106 107 111 113 115 117
Finiteness, isomorphism classes of curves 103
Finiteness, l-adic representations 112
Finiteness, polarizations 103
Finiteness, principally polarized abelian varieties 117
Finiteness, rational points 12 13 37—39 130 187
Finiteness, rational points by Parshin method in function field case 187
Finiteness, rational points in division groups 37—38
Finiteness, rational points in Eisenstein quotient 130
Finiteness, rational points on modular curves 130
Finiteness, rational points on toruses 37—38
Finiteness, Shafarevich — Tate group 89 253 “Mordell “Shafarevich “Torus” “Unit
First kind 11 136
First Main Theorem 194
Forms in 10 variables 247
Fourier coefficients 130
Franke 260—262
Frey polynomial 51
Frey’s idea for Fermat 132 134 135
Frobenius automorphism 84 85 95 113 114 132 133
Frobenius automorphism, isogeny 84
Fujimoto 183 184
Function field 4 12
Function field case 12 18 23 24 27 28 39 45—47 62 74 76—82 92 104 145 178 187 192 221
Function field case, abelian varieties 39 187
Function field case, Birch — Swinnerton — Dyer 92
Function field case, Mordell conjecture 62 143—162 230
Function field case, product formula 52
Function field case, quadratic form 74
Function field case, Shafarevich conjecture 104
Function field case, torsion 27
Functional equation 98
Galois groups 39 42
Galois groups of torsion points 39 83 132 238
Galois representations 39 83 132
Gauss — Manin connection 154—161
Gauss — Manin connection on abelian varieties 158
Gelfond 235
General (type) variety 15 17
General position 183 215
Generalized Jacobian 106
Generalized Szpiro conjecture 51
Generic complete intersection 181
Generic fibration 18 20—23
Generic fibration, Chatelet surface 257
Generic fibration, Fermat 22 23
Generic fibration, K3 surface 20
Generic fibration, Kummer surface 20
Generic fibration, quintic threefold 21
Generic hypersurface 21 181
Generic quintic threefold 21
Generically surjective 5 24
Genus 10
Genus formula in terms of degree 11
Geometric canonical height 146
Geometric conditions for diophantine bounds 176
Geometric fiber 149
Geometric genus 14 15
Geometric logarithmic discriminant 146
Gillet — Soule 173—175 230 232
Gillet — Soule theorem 174
Gillet — Soule theory 173—175 230 232
Global degree 53 168
Goldfeld on rank 28
Good completion of Neron model 80 82
Good reduction 68—70 91 103—106 113
Grauerfs construction 147—149
Green and Fujimoto theorem 183
Green example of Brody but not Kobayashi hyperbolic 183
Green function 164 165 209
Green — Griffiths 20 179 180 182 186
Green — Griffiths, Bloch conjecture 182
Green — Griffiths, conjecture 179 180
Greenberg functor 259
Greenleaf theorem 248
Griffiths — King on Nevanlinna theory 201 204
Griffiths, complement of a large divisor 226
Griffiths, function 185
Gross on Birch — Swinnerton-Dyer 94—96
Gross — Zagier theorems 139—142
Grothendieck on semistable reduction 70
Group variety 16 20 67 255—258 “Toruses”)
Hall conjecture 49
Harder 255
Hardy — Littlewood circle method 248
Hartshorne conjecture 20
Hasse conjecture 98
Hasse conjecture, eigenvalues of Frobenius 85
Hasse principle 248—258
Hasse principle, hyperbolicity connection 254
Hasse principle, non-singular 248
Hasse — Deuring l-adic representations 83
Heath — Brown 247
Hecke, algebra 129
Hecke, correspondence 129
Hecke, involution 129 139
Hecke, operators 130
Heegner point 138—141
Height 43 51 53—67 70 72—82 85 86 99 100 117—123 146 152 153 168 169 171 193—200 202 203 222 224 227 233—243 252 260
Height, algebraic families 62 74 76—82
Height, algebraically equivalent to zero 59
Height, Arakelov degree 168 169
Height, as a norm 73 85 86 236 241 242
Height, associated with divisor class or line sheaf 58—61 194—196
Height, bounded 56—58 62—67 99 233
Height, canonical 63 64 67 146 169 202
Height, canonical coordinates on abelian varieties 77
Height, Cartan — Nevanlinna 193—198
Height, Faltings 74 117—123 227 238
Height, finite extensions 51
Height, inequalities see below “Upper and lower bounds”
Height, intersection numbers 169
Height, Lie 119
Height, lower bound 73 74 100
Height, Nevanlinna theory 193—200 202
Height, normalized 260
Height, pairing 72—76
Height, transform 203
Height, upper bound 62—67 99 100 152 153 160 170 171 222 224 227 “Modular “Properties “Regulator”)
Hensel’s Lemma 249
Hermite theorem 99 114
Hermitian, manifold 177
| Hermitian, vector sheaf 166—168
Hilbert irreducibility 40—42
Hilbert irreducibility, application 42 162
Hilbert subset 41
Hilbertian 41
Hindry theorem 37 38
Hindry — Silverman lower bound on height 74
Hirata — Kohno theorem 237
Hodge index 168
Holomorphic special set 179 182
Homomorphisms of abelian varieties 26
Hooley 247
Horizontal differentiation 156
Humbert 103
Hurwitz genus formula 37 105
Hyperbolic 16 17 25 177—192 225—228 254
Hyperbolic algebraicity 16 17 179
Hyperbolic Brody 179
Hyperbolic complement of a large divisor 226
Hyperbolic Hasse principle connection 254
Hyperbolic hypersurfaces 180
Hyperbolic Kobayashi 178—181 184
Hyperbolic metric on disc 177
Hyperbolic Mordellic connection 25 179 186
Hyperbolic Parshin’s method 187
Hyperbolically imbedded 190—192 225
Hyperbolicity, ampleness connection 181
Hyperbolicity, integral points connection 225—227
Hyperplanes in projective space, complementary set 183
Hypersurface 4
Hypersurface generic 21
Ideal class group 55
Igusa zeta function 250
Imbedding 5
Index, formulas 141
Index, in Schneider — Roth theorem 229
Index, in Vojta’s theorem 231
Index, of Heegner point 140
Inertia group 84 112
Infinite descent 85
Integral points 22 189 217—222 226
Integral points, and hyperbolicity 22 189 226
Integral points, complement of 2n + 1 hyperplanes in general position 221
Integral points, Faltings theorem on abelian varieties 220
Integral points, function field case 221
Integral points, higher dimensional function field case 189 221
Integralizable 217
Intersection 144 167 209
Intersection number 144 167
Intersection pairing 144
Intersection theory and Weil functions 209
Involution on modular curve 129
Iskovskih surface 253
Isogeny 28 34 35 108 113 121 122 128 238—239
Isogeny, bounds by Masser — Wustholz 121 122 238 239
Isogeny, bounds by Mazur 128
Isogeny, bounds on degree by Kamienny 28
Isogeny, problem 121
Isogeny, theorem 108
Isomorphism classes of toruses 107 126
Iwasawa theory 30
Jacobian 32 102 103
Jensen’s formula 193
Jouanolou theorem 148
K3 surface 20 23
Kamienny on torsion 28
Kanevsky 250
Kato — Kazumaki conjecture 247
Kawamata fibration 36
Kawamata fibration, Bloch conjecture 182
Kawamata fibration, structure theorem 35 182
Khintchine function 198 199 223
Khintchine function, theorem 213 214 234
Kneser 255
Kobayashi chain 178
Kobayashi chain, hyperbolic 178 184
Kobayashi chain, semidistance 178 186
Kobayashi conjecture on hyperbolic hypersurfaces 180
Kobayashi conjecture on hyperbolic hypersurfaces, hyperbolicity 177—192 225 226
Kobayashi conjecture on hyperbolic hypersurfaces, hyperbolicity and (1, l)-forms 185 186
Kobayashi conjecture on hyperbolic hypersurfaces, hyperbolicity and pseudo ample cotangent bundle 181
Kobayashi conjecture on hyperbolic hypersurfaces, theorem on ample cotangent bundle 181
Kobayashi — Ochiai 24 25 192
Kodaira criterion for pseudo ample 9 20
Kodaira — Spencer map 157—161
Koizumi — Shimura theorem 113
Kollar 20
Kolyvagin theorem 89 139
Kubert on torsion points 28
Kubert — Lang 37 141 225
Kummer surface 20
l-adic representation 82—85 107—115 238
L-function, abelian variety 91—98
L-function, elliptic curve 97 98 139—142
L-function, local factor 95 97
Lander and Parkin 23
Lang conjectures, Ax theorem 182
Lang conjectures, bound for regulator and Shafarevich — Tate 99
Lang conjectures, diophantine 15—20
Lang conjectures, diophantine approximation 233—237
Lang conjectures, division points 37
Lang conjectures, exceptional set in Vojta 67
Lang conjectures, Fermat unirationality 22
Lang conjectures, finitely generated groups 36
Lang conjectures, function field case 13
Lang conjectures, Greenleaf theorem 248
Lang conjectures, Green’s theorem 182
Lang conjectures, hyperbolic imbedding 190 191
Lang conjectures, hyperbolicity 17 179 181 186
Lang conjectures, integral points 50 220 225
Lang conjectures, lower bound on height 73 74 100 243
Lang conjectures, Mordellic property 15 16 25 36 179
Lang conjectures, pseudo Mordellic 17 180 181
Lang conjectures, reduction to ordinary abelian varieties 162
Lang conjectures, upper bound on height 99
Lang — Neron theorems 27 32 74 75
Lang — Neron theorems and theorem of the kernel 159
Lang — Stark conjecture 50
Lang — Tate exact sequence for principal homogeneous spaces 87
Lang, error term in Nevanlinna theory 199—201 203
Lang, on integral points 218
Lang, theorem over finite fields 87
Lange on polarizations 103
Langlands — Eisenstein series 260
Laplace operator 173
Lattice points in expanding domain 57
Laurent theorem 38
Lehmer conjecture 243
Level n structure 118
Level of modular form 130 131 133—135
Level of modular form of representation 133—135
Lewis theorem on forms in 10
Lewis theorem on forms in variables 247
Liardet theorem 37
Lie determinant 116
Lie height 119
Linear group varieties 256
Linear torus 37
Linearly equivalent 6
Lipschitz parametrizable 57
Local complete intersection 145
Local degree 53
Local diophantine conditions 176
Local exact sequences 251
Local factor of L-function 95
Local parameter 10
Local ring 5
Local specialization principle 258—259
Locally bounded 207
Logarithm on Lie groups 234—239
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