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Lang S. Ч Diophantine Geometry
Lang S. Ч Diophantine Geometry

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Ќазвание: Diophantine Geometry

јвтор: Lang S.

јннотаци€:

Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the braod scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication... Although in the series of number theory, this volume is on diophantine geometry, the reader will notice that algebraic geometry is present in every chapter. ...The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1997

 оличество страниц: 316

ƒобавлена в каталог: 20.09.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Fermat, fibrations      23
Fermat, Frey elliptic curve      132 135
Fermat, hypersurface      22 23
Fermat, modular curve correspondence      23 225
Fermat, RibetТs reduction of last theorem to Taniyama Ч Shimura      132
Fermat, Taniyama Ч Shimura implies Fermat      132
Fermat, theorem for polynomials      48
Fermat, unirational for low degree?      22 23
Fermat, VojtaТs conjecture implies Fermat asymptotic      64
Fibration      18 20Ч24 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      26Ч32 36Ч40 240Ч243
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      106Ч109 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 37Ч39 130 187
Finiteness, rational points by Parshin method in function field case      187
Finiteness, rational points in division groups      37Ч38
Finiteness, rational points in Eisenstein quotient      130
Finiteness, rational points on modular curves      130
Finiteness, rational points on toruses      37Ч38
Finiteness, Shafarevich Ч Tate group      89 253 УMordell УShafarevich УTorusФ УUnit
First kind      11 136
First Main Theorem      194
Forms in 10 variables      247
Fourier coefficients      130
Franke      260Ч262
Frey polynomial      51
FreyТs 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 45Ч47 62 74 76Ч82 92 104 145 178 187 192 221
Function field case, abelian varieties      39 187
Function field case, Birch Ч Swinnerton Ч Dyer      92
Function field case, Mordell conjecture      62 143Ч162 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 Ч Manin connection      154Ч161
Gauss Ч 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 20Ч23
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 Ч Soule      173Ч175 230 232
Gillet Ч Soule theorem      174
Gillet Ч Soule theory      173Ч175 230 232
Global degree      53 168
Goldfeld on rank      28
Good completion of Neron model      80 82
Good reduction      68Ч70 91 103Ч106 113
Grauerfs construction      147Ч149
Green and Fujimoto theorem      183
Green example of Brody but not Kobayashi hyperbolic      183
Green function      164 165 209
Green Ч Griffiths      20 179 180 182 186
Green Ч Griffiths, Bloch conjecture      182
Green Ч Griffiths, conjecture      179 180
Greenberg functor      259
Greenleaf theorem      248
Griffiths Ч King on Nevanlinna theory      201 204
Griffiths, complement of a large divisor      226
Griffiths, function      185
Gross on Birch Ч Swinnerton-Dyer      94Ч96
Gross Ч Zagier theorems      139Ч142
Grothendieck on semistable reduction      70
Group variety      16 20 67 255Ч258 УTorusesФ)
Hall conjecture      49
Harder      255
Hardy Ч Littlewood circle method      248
Hartshorne conjecture      20
Hasse conjecture      98
Hasse conjecture, eigenvalues of Frobenius      85
Hasse principle      248Ч258
Hasse principle, hyperbolicity connection      254
Hasse principle, non-singular      248
Hasse Ч Deuring l-adic representations      83
Heath Ч Brown      247
Hecke, algebra      129
Hecke, correspondence      129
Hecke, involution      129 139
Hecke, operators      130
Heegner point      138Ч141
Height      43 51 53Ч67 70 72Ч82 85 86 99 100 117Ч123 146 152 153 168 169 171 193Ч200 202 203 222 224 227 233Ч243 252 260
Height, algebraic families      62 74 76Ч82
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      58Ч61 194Ч196
Height, bounded      56Ч58 62Ч67 99 233
Height, canonical      63 64 67 146 169 202
Height, canonical coordinates on abelian varieties      77
Height, Cartan Ч Nevanlinna      193Ч198
Height, Faltings      74 117Ч123 227 238
Height, finite extensions      51
Height, inequalities      see below УUpper and lower boundsФ
Height, intersection numbers      169
Height, Lie      119
Height, lower bound      73 74 100
Height, Nevanlinna theory      193Ч200 202
Height, normalized      260
Height, pairing      72Ч76
Height, transform      203
Height, upper bound      62Ч67 99 100 152 153 160 170 171 222 224 227 УModular УProperties УRegulatorФ)
HenselТs Lemma      249
Hermite theorem      99 114
Hermitian, manifold      177
Hermitian, vector sheaf      166Ч168
Hilbert irreducibility      40Ч42
Hilbert irreducibility, application      42 162
Hilbert subset      41
Hilbertian      41
Hindry theorem      37 38
Hindry Ч Silverman lower bound on height      74
Hirata Ч 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 177Ч192 225Ч228 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      178Ч181 184
Hyperbolic metric on disc      177
Hyperbolic Mordellic connection      25 179 186
Hyperbolic ParshinТs method      187
Hyperbolically imbedded      190Ч192 225
Hyperbolicity, ampleness connection      181
Hyperbolicity, integral points connection      225Ч227
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 Ч Roth theorem      229
Index, in VojtaТs theorem      231
Index, of Heegner point      140
Inertia group      84 112
Infinite descent      85
Integral points      22 189 217Ч222 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 238Ч239
Isogeny, bounds by Masser Ч 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
JensenТs formula      193
Jouanolou theorem      148
K3 surface      20 23
Kamienny on torsion      28
Kanevsky      250
Kato Ч 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      177Ч192 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 Ч Ochiai      24 25 192
Kodaira criterion for pseudo ample      9 20
Kodaira Ч Spencer map      157Ч161
Koizumi Ч Shimura theorem      113
Kollar      20
Kolyvagin theorem      89 139
Kubert on torsion points      28
Kubert Ч Lang      37 141 225
Kummer surface      20
l-adic representation      82Ч85 107Ч115 238
L-function, abelian variety      91Ч98
L-function, elliptic curve      97 98 139Ч142
L-function, local factor      95 97
Lander and Parkin      23
Lang conjectures, Ax theorem      182
Lang conjectures, bound for regulator and Shafarevich Ч Tate      99
Lang conjectures, diophantine      15Ч20
Lang conjectures, diophantine approximation      233Ч237
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, GreenТs 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 Ч Neron theorems      27 32 74 75
Lang Ч Neron theorems and theorem of the kernel      159
Lang Ч Stark conjecture      50
Lang Ч Tate exact sequence for principal homogeneous spaces      87
Lang, error term in Nevanlinna theory      199Ч201 203
Lang, on integral points      218
Lang, theorem over finite fields      87
Lange on polarizations      103
Langlands Ч 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 133Ч135
Level of modular form of representation      133Ч135
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      258Ч259
Locally bounded      207
Logarithm on Lie groups      234Ч239
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