Lang S. — Diophantine Geometry :: 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

Lang S. — Diophantine Geometry

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Diophantine Geometry

Автор: Lang S.

Аннотация:

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:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 316

Добавлена в каталог: 20.09.2008

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

Предметный указатель

property      245—249
and       12 126
-degree      173
      82 94
      83
      127—131
and       127
abc conjecture      29 47 49 65
Abelian logarithm      237
Abelian varieties      16 20 25—42 68—100 101—122 158—162 181—183 220 221 232 236—239
Abelian varieties, equations for      26 77 “Birch “Descent” “Faltings” “Finiteness” “Function “Gauss “Jacobian” “l-adic “Lang “Manin’s “Masser “Moduli” “Mordell “Neron “Neron “Parshin” “Polarization” “Rank” “Raynaud” “Semisimplicity” “Semistable” “Subvarieties” “Tate “Theorem “Torsion “Trace
Absolute case      12
Absolute conjecture      67
Absolute norm      55
Absolute value      44
Adams type for e      214
Adeles      93
Adjunction formula      168
Admissible metric      165
Affine bounded      207
Affine coordinate ring      4
Affine coordinate ring, coordinates and integral points      217
Affine variety      2
Ahlfors on Nevanlinna theory      199 203
Ahlfors — Schwarz lemma      185
Ahlfors — Shimizu height      200
Albanese variety      31 32
Albert — Brauer — Hasse — Noether theorem      252—253
Algebraic equivalence      30 33
Algebraic families      12 18 23—27 28 62 74—82 118—121 158—162 178 187 189 192 221
Algebraic families of abelian varieties      27 28 74—82 118—121 158—162 189
Algebraic families of heights      76—82
Algebraic families of pseudo-canonical varieties      24 25
Algebraic families, split      12 24 25 62 78 79 178 192 “Function “Manin “Silverman
Algebraic integers      54
Algebraic point      3
Algebraic point in Vojta’s conjecture      50 63—67 222—225
Algebraic special set      16 182
Algebraically hyperbolic      16 17 179
ample      7 11—15 20 22 67 181 198
Ample, anti-canonical class      19 20 67
Ample, canonical class      14 15 18 22 198
Ample, cotangent bundle      181
Ample, vector sheaf      20
Analytic torsion      173 175
Anticanonical class      15 19 20 67 169 245 258—262
Anticanonical varieties      15 259—262
Arakelov, degree      168
Arakelov, height      169
Arakelov, inequality      151
Arakelov, metric      165
Arakelov, Picard group      167
Arakelov, Shafarevich conjecture in function field case      104
Arakelov, theory      71 163—171 228 230 231
Arakelov, volume form      166
Arithmetic Chern character      173
Arithmetic Chow group      174
Arithmetic discriminant      64 171
Arithmetic discriminant and Vojta’s inequality      171
Arithmetic Euler characteristic      173
Arithmetic Picard group      167
Arithmetic surface      166
Arithmetic Todd class      173
Arithmetic variety      171
Artin theorem on local specialization      259
Artin — Tate      250 253
Artin — Winters      150
Artin, conductor      71
Artin, conjectures on fields      246—247
Ax theorems, one-parameter subgroups      182
Ax theorems, quasi-algebraic closure      246
Ax — Kochen theorem      247
Baily — Borel compactification      118
Baker      235 237 239 240
Baker — Feldman inequality      235
Basic Hilbert subset      41
Basic isogeny problem      121
Batyrev      20 262
Batyrev — Manin conjectures      260—262
Batyrev — Manin conjectures, relation with Vojta conjecture      261
Beilenson Bloch conjectures      34
Biduality      33
Birational map      5
Birationally equivalent      5
Birch      148 248
Birch — Swinnerton — Dyer conjecture      34 91 92 94—96 98 136 137 139—140
Birch — Swinnerton — Dyer conjecture, Coates — Wiles      136
Birch — Swinnerton — Dyer conjecture, Gross — Zagier      139—142
Bismut — Vasserot      174 232
Bloch (Andre) conjecture      182
Bloch (Spencer) conjectures      34
Bogomolov      20 151
Bombieri simplification of Vojta’s proof      233
Borel’s theorem      183
Bosch      259
Bounded degree      56 63 64 204 222 223
Bounded degree, denominator      217
Bounded degree, generated group      240—243
Bounded degree, height      see “Height upper
Brauer group      250—258
Brauer group, birational invariant      252
Brauer group, exact sequence      255
Brauer group, unramified      252
Brauer — Grothendieck group      250 252
Brauer — Grothendieck group, specialization      252
Breen      80
Brody hyperbolic      178 179 183 184 225 226
Brody — Green hypersurface      22 181 186
Brody’s theorem      179
Brownawell-Masser      66
Brumer — McGuinness on average rank      28
Bryuno      214
Canonical bundle      185
Canonical class      11 14 20 21 119 146 151 152 197
Canonical class, in higher dimension      14
Canonical class, inequalities      151 152
Canonical class, on a curve      11
Canonical class, on moduli space      119
Canonical class, on projective space      14 197
Canonical class, relative      146
Canonical class, zero      19—21 23
Canonical height      63 64 67 146 169
Canonical height in Nevanlinna theory      202
Canonical metric      165 166
Canonical sheaf      119 145 146 169 170 228 259
Canonical sheaf of an imbedding      145 146 169
Canonical variety      15
Carlsson — Griffiths on Nevanlinna theory      201
Cartan — Nevanlinna height      194
Cartan’s theorem      197—198
Cartier divisor      6 14
Cartier divisor, divisor class group      6
Cassel — Guy example      254
Cassels — Tate pairing      89
CC inequalities      151 152
Chabauty      36 38
Chai on cubical sheaves      80 82
Chai — Faltings      118 120 122
Chai’s theorem of the kernel      158
Characteristic polynomial      85
Chatelet — Weil group      87 88
Chatelet, Brauer variety      256
Chatelet, surface      22 256 257
Chern form      184 202
Cherry on Nevanlinna theory      204 223
Chevalley — Weil theorem      224
Chevalley’s theorem on quasi-algebraic closure      246
Chow group      7 33 174
Chow group in higher codimension      34
Chow trace      26 (see also “Lang — Neron” “Trace

Chow — Lang      69 103
Circle method      248
Class field theory      105
Clemens curves      21 34
Co — Lie determinant      116 118
Coates — Wiles theorem      136
Cocycle      153
Coleman’s account of Manin’s method      153—161
Colliot — Thelene      249—258
Colliot — Thelene, conjecture      254
Compact case of Vojta conjecture      67
Complete intersection      4
Complex multiplication      29 39 136
Complex torus      125
Complex torus, isomorphism classes      126
Complexity of divisor      203
Conductor      51 71 97—99
Conductor of elliptic curve      97—99 (see also “Modular elliptic curves”)
Congruent numbers      135
Connected component      31 33
Connected component, Neron model      70 79—81 98
Connection      154
Conormal sheaf      145 169
Constant field      12
Counting function      193 202 211
Counting, algebraic integers      57
Counting, points      58 61 73 260—262
Counting, units      57
Coverings, applied to diophantine approximations      219 222
Coverings, descent and heights      37 85 160
Coverings, Nevanlinna theory      204
Coverings, Parshin construction      104—106
Coverings, ramified      104—105 224 225
Coverings, torsion points      39
Coverings, X_0(N)X_1(N)$      128
Cubic forms      22 247 250
Cubical sheaves      80 81
Curvature      185 186
Cuspidal group      128
Cuspidal group, ideal      129
Cusps      127
Cycles      31 32 254
Cyclotomic character      133
Cyclotomic extensions      29 247
Cyclotomic units      141
d(F) or d(P)      55
Davenport      48 49 247
de Franchis theorem      13 24
De Rham cohomology      153—160
Decomposition group      83 88 112
Degree of canonical sheaf      152
Degree of divisor on a curve      9
Degree of hypersurface      4
Degree of isogeny      35
Degree of line sheaf      144
Degree of metrized line sheaf      116
Degree of polarization      35
Degree on a singular curve      144
Degree with respect to Riemann form      238 (see also “Isogeny” “Polarization”)
Degree, Arakelov      168
Deligne on Faltings proof      120
Deligne on L-function      92
Deligne — Mumford      150
Deligne — Serre representation      132
Demjanenko — Manin on split function field case      79
Demjanenko, estimate of Neron height      72
Demjanenko, fibering of Fermat surface      23
Descent      85 90 91 160 219
Descent in coverings      160 219
Descent with Selmer groups      90
Determinant of vector sheaf      144
Diagonal hyperplane      183
Different      120
Differential form      10
Differentials      115
Differentials of first kind      11 136
DIMENSION      4
Diophantine approximation on toruses      233—243
Diophantine approximation to numbers      213—216
Dirichlet box principle      234
Discriminant      50 55 69
Discriminant in coverings      224
Discriminant of elliptic curve      69 96
Distance      177
Division group      37 38 161 Raynaud
Divisor      6
Divisor class group      6 33
Divisor classes and heights      58—61 194—196
Divisor classes and Neron functions      213
Dobrowolski      243
Dolbeault operator      172
Dual variety      33
Dyson’s lemma      229 231 232
Effective divisor      6
Effective divisor class      7
Eigenform      131 132
Eigenvalues of Frobenius      85 91 131
Eigenvalues of Laplacian      173 175
Eisenstein ideal      129
Eisenstein ideal, quotient      129
Eisenstein ideal, series      260
Elkies example of integral points      50
Elkies on Fermat hypersurface      23
Elliptic curve      12 21 23 25—27 49 50 96 132 135 139—142 162
Elliptic curve, conductor      97 98
Elliptic curve, diophantine approximation      235 236
Elliptic curve, fibers of family      21 23
Elliptic curve, Frey      132 135
Elliptic curve, height of generators      99 100
Elliptic curve, integral points      50
Elliptic curve, isomorphism      96
Elliptic curve, L-function      97—98 137—142
Elliptic curve, minimal discriminant      97
Elliptic curve, modular      130—142
Elliptic curve, periods      93 95 97 125 236
Elliptic curve, rank      28 42 92 139—142
Elliptic curve, rank one over the rationals      137—142
Elliptic curve, Tate curve      162 (see also “Torsion points”)
Error function in Nevanlinna theory      203 224
Error terms in second main theorem      199—204 224
Error terms in second main theorem, Lang conjecture      200
Esnault — Viehweg inequality      152
Esnault — Viehweg inequality on Roth theorem      229
Euler characteristic      172
Euler characteristic, arithmetic      173
Euler on Fermat      22
Euler product for a variety      91
Exact sequence, de Rham cohomology      156
Exact sequence, group cohomology      88 250 255
Exact sequence, Lang — Tate      87
Exact sequence, Selmer and Shafarevich — Tate group      88—90
Exceptional set in Vojta conjecture      67
Exceptional set in Vojta conjecture in Schmidt — Vojta theorem      215 222
Exponential on Lie groups      236
Faltings, canonical height      119
Faltings, finiteness of l-adic representations      114
Faltings, finiteness of rational points      12 18 36 230 232
Faltings, formula for the degree      120
Faltings, height      74 117—123 238
Faltings, inequality on abelian varieties      220 237
Faltings, integral points on abelian varieties      220 221
Faltings, positivity of canonical sheaf      170
Faltings, semisimplicity and Tate conjecture      111—115
Faltings, stable height      117 238
Faltings, subvariety of abelian variety      36
Fano variety      260
Fermat      11 22 23 48 62 64 132 135 181 225
Fermat, Brody — Green perturbation      181
Fermat, curve      11
Fermat, Euler      22

1 2 3 4

О проекте