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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
Logarithmic discriminant      55 146
Logarithmic discriminant, height      43
Lower bound conjectures      74 100 243
Lu Ч Yau      180
Maehara      24
Mahler      58 217 220
Manin Ч Mumford conjecture      37 38
Manin Ч Zarhin equations for abelian varieties      26 77
Manin Ч Zarhin equations for abelian varieties, height with canonical coordinates      77
Manin, Brauer group      253
Manin, constant      140 141
Manin, counting      260Ч262
Manin, cubic surfaces      23 48
Manin, elliptic curves      253
Manin, function field case of Mordell      13 37 153Ч161
Manin, letter      158
Manin, obstruction      250 253Ч258
Manin, unirationality      23
Mason theorem      48 65
Mason theorem in several variables      66
Masser lower bound on height      74 240 243
Masser Ч Oesterle abc conjecture      48
Masser Ч Wustholz theorem      121 238Ч239
Masser Ч Wustholz theorem, replacement of Raynaud theory      122
MayТs theorem      58
Mazur, Eisenstein quotient      129
Mazur, points in cyclotomic extensions      29
Mazur, torsion group      28 127Ч130 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 Ч Persson on torsion      27
Miyaoka      151
Miyaoka Ч Mori      20
Modular elliptic curve      132 136 138Ч142
Modular representation      133 134
Modular units      37 141
Moduli space      118 119
Mordell conjecture      12 106
Mordell conjecture, Faltings proof      107Ч121
Mordell conjecture, function field case      13 143Ч162
Mordell conjecture, VojtaТs proof      230
Mordell objection to Riemann Ч Roch      230
Mordell Ч Weil, group and units      142
Mordell Ч Weil, in abelian extensions      29
Mordell Ч Weil, Shioda lattice      75
Mordell Ч Weil, theorem      26 27 УSpecializationФ УTorsion
Mordellic      15 16 25 36 179
Moret Ч Bailly      170
Mori Ч Mukai      20
Mori, on Hartshorne conjecture      20
Mori, proof of UenoТs 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 Ч Nori theorem      103
Neron Ч Severi group      30 32Ч34 77 79 149 261
Neron Ч Tate height      72Ч75 82 85 86 241 242
Neron Ч Tate height and Weil height      72
Neron Ч Tate height, estimates by Demjanenko      72
Neron Ч Tate height, estimates by Zimmer      72
Neron Ч Tate norm      73
Neron Ч Tate norm, quadratic form      72Ч75
Neron, algebraic families of Neron functions      213
Neron, function      210 212
Neron, model      19 69Ч71 79Ч82 94 95 115Ч117 120
Neron, pairing      212
Neron, rank      41 42
Neron, specialization theorem      41
Neron, symbol      212
Neron, theorem on Mordell Ч Weil      26
Nevanlinna theory      192Ч204
Nevanlinna theory for coverings      204
Newton approximation      249 259
Noether and Galois groups      42
NoetherТs formula      152 168
Noguchi      36 183 184 190Ч192
Non-degenerate      202
Non-singular      4
Non-singular Hasse principle      248Ч258
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 Ч Kawamata fibrations      36 (see also УKobayashi Ч OchiaiФ)
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 Ч Arakelov proof of Shafarevich conjecture in function field case      104
Parshin, construction      104 105 170
Parshin, hyperbolic method      149 187Ч189
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 Ч 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 УLangeФ УMasser УModuli УTorelliФ)
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      85Ч91 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      194Ч196
Properties of height in number theory      58Ч61
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 179Ч181
Pseudo hyperbolic      180Ч181
Pseudo Mordellic      17 180Ч181
Pseudofication      15 179Ч181
Pythagorean triples      135
Quadratic form      see УNeron Ч TateФ
Quadratic forms in 9 variables      249
Quasi function      207
Quasi-algebraic closure      245Ч248 259
Quasi-projective variety      3
Quintic threefold      21 34
RamanujanТs taxicab point      23
Ramification, counting function      197 199 201Ч204
Ramification, divisor      196 202
Ramification, order      196 105
Rank, average      28
Rank, cyclotomic extensions      29
Rank, Demjanenko Ч Manin criterion      79
Rank, elliptic curve      28 42 92 139Ч142
Rank, finitely generated group      240Ч243
Rank, generic case      27
Rank, high rank by Neron specialization      42
Rank, Mestre      28
Rank, Mordell Ч Weil group      28 92 139Ч142 237
Rank, Neron Ч Severi group      261
Rank, rank 1 over the rationals      138Ч141 (see also УBirch Ч Swinnerton Ч DyerФ УBrumer УNeronФ УShafarevich УZagier
Rational curves      16 18Ч20 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, ParshinТs 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 Ч Weil group      93 98
Relations      242
Relative canonical class      146
Relative case      12
Relative cohomology group      154
Relative Gauss Ч Manin connection      155
Relative tangent sheaf      173
Relatively algebraically closed      258
Representation, finite at a prime      134 (see also УGalois representationФ Уl-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 Ч Devaney Ч Metropolis      214
Riemann form      209
Riemann Ч Roch      173Ч175 214 230 232 233
Riemann Ч Roch in Roth theorem      214
Riemann Ч Roch in VojtaТs proof      230
Riemann Ч Roch, objection by Mordell      230 (see also УBombieriФ УGillet
Robba      259
Rosenlicht      106
Roth theorem      215
Roth theorem, geometric version      218
Ru Ч Wong theorem      221
Rubin on Shafarevich Ч Tate group      89
S-integers      214
Saito, S.      71
Saito, T.      254
Salberger      249 255
Samuel proof in characteristic p      161
Sansuc      249Ч258
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      196Ч204
Selmer, example      89
Selmer, group      88Ч91
Semiabelian variety      36 37 39
Semiabelian variety, Noguchi theorem      183
Semisimplicity of l-adic representations      107Ч111 113Ч115
Semisimplification      133
Semistable abelian variety      70 71
Semistable curve      150
Semistable reduction      70 71 117 120 121 149Ч151
Serre Ч 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 Ч Brauer      256
Shafarevich conjecture      104 106 111
Shafarevich conjecture, implied by Vojta conjecture      227
Shafarevich conjecture, implies Mordell      106
Shafarevich Ч Tate, exact sequence      88
Shafarevich Ч Tate, example of high rank in function field case      28 92
Shafarevich Ч Tate, group      88Ч91 94 96 98 99 139 140 253Ч255
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 Ч Weil Ч Lang Ч 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 Ч Tate theorem      77
Simple normal crossings      196 202 223
Siu      198
Soule      168 173Ч175 232
Sp (Special Set) questions      18 245
Special set      16 17Ч23 67 179 182 245
Special set and exceptional set      67
Special set, holomorphic      179
Special set, holomorphic and algebraic are equal      182
Special variety      17Ч20
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 181Ч183 220 232
Subvarieties of abelian varieties, Ax theorem      182
Subvarieties of abelian varieties, Faltings theorem      36 220
Subvarieties of abelian varieties, GreenТs theorem      182
Subvarieties of abelian varieties, special set      36
1 2 3 4
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