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Lang S. — Diophantine Geometry

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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.

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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

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Предметный указатель

Subvariety      3
Sum formula      45
Support      7
Swan conductor      71
Swinnerton — Dyer      249 257
Swinnerton — Dyer on Fermat      22 (see also “Birch — Swinnerton — Dyer”)
Szpiro, conjecture      51
Szpiro, positivity of canonical sheaf      170
Szpiro, Raynaud theorem connection      170
Tangent sheaf      173
Taniyama conjectures      131
Taniyama — Shimura conjecture      131 134 136 138
Taniyama — Shimura implies Fermat      134
Tate, duality of cohomology over p-adic fields      87
Tate, module      82
Tate, property      107 109 111 112 115
Tate, theorem on algebraic families of heights      81 82 “Shafarevich “Silverman
Terjanian example      247
Theorem of the kernel      158 159
Theta divisor      102
Theta functions      209
Thue — Siegel theorem      220 228 232
Torelli’s theorem      102 103
Torsion points      27—29 39 82—85 127—130 138 238
Torsion points, diophantine approximation      238
Torsion points, function field case      27
Torsion points, Galois group      39
Torsion points, l-adic representations      82—85
Torsion points, uniformity conjecture      28 (see also “Kamienny” “Kubert” “Masser “Mazur” “Miranda
Torus      37 38 71 233—239 “Semiabelian
Totally geodesic      189
Trace of an abelian variety (Chow)      26 74
Trace of Frobenius      97 113 114 132
Translation on Neron model      80
Tschinkel      260—262
Tsen’s theorem      246
Tsfasman      250
Tunnell on congruent numbers      135—137
Twisted elliptic curve      139
Type for a number      213 216
Type of meromorphic function      200 216
Ueno fibration      35 36
Ueno — Kawamata fibration      36 183
Ulmer on L-function      92
Unigrouped      20
Unipotent group      71
Unirational      6 16 20 22 244 257
Uniruled      20
Unit equation      37 66 219 220
Units counting      57
Unramified, Brauer group      252
Unramified, Chevalley — Weil theorem      224
Unramified, correspondence between Fermat and modular curves      225
Unramified, extension      247 251
Unramified, good reduction      113
Unramified, representation      112 (see also “Coverings”)
Upper half plane      124
Valuation      44
van de Ven      151
van den Dries      259
Variety      2
Vector sheaf      144
Very ample      7

Very canonical      15
Viola      229 231 233
Vojta theorems      147 152 171 174—175 193—195 197—198 201 204 215 216 226 230—232
Vojta theorems, (1, l)-form theorem      201
Vojta theorems, dictionary      193—195
Vojta theorems, estimate for discriminants, generalized Chevalley — Weil      224
Vojta theorems, estimates for sections      174—175
Vojta theorems, improvement of Cartan’s theorem      197—198
Vojta theorems, improvement of Schmidt theorem      215 216 222
Vojta theorems, inequality and Nevanlinna theory      204
Vojta theorems, inequality in function field case      147 152
Vojta theorems, inequality with arithmetic discriminant      171
Vojta theorems, integral points      226
Vojta theorems, proof of Faltings’ theorem (Mordell conjecture)      230—232
Vojta’s conjectures      50 63 64 67 222—224 226—227
Vojta’s conjectures, (1, l)-form conjecture and Shafarevich conjecture      226 227
Vojta’s conjectures, compact case      67
Vojta’s conjectures, exceptional set      67 215 216 222
Vojta’s conjectures, Fermat curve      64
Vojta’s conjectures, general      222—224
Vojta’s conjectures, higher dimension      66
Vojta’s conjectures, imply abc conjecture      64
Vojta’s conjectures, relation to Batyrev — Manin      261
Vojta’s conjectures, uniformity with respect to the degree      63 64 204 222 223
Voloch, division points in characteristic p      161 162
Voloch, unit equation      66
Volume      166 172 185
Waldschmidt      241
Waldspurger’s theorem      137
Weierstrass functions      25
Weight 3/2      136 141
Weight 3/2 of a modular form      136
Weil, algebraic equivalence criteria      33
Weil, divisor      6
Weil, eigenvalues of Frobenius      85 114 249
Weil, function      164 192 198 207 209 210
Weil, function as intersection number      209
Weil, function associated with a hyperplane      216
Weil, height      45
Weil, height as sum of local Weil functions      210
Weil, l-adic representations      83
Weng’s comments on Gillet — Soule      174
Wild ramification      71
Wong on integral points      221
Wong on integral points on Nevanlinna theory      199 201 203
wronskian      197
Wronskian method in Roth theorem      229
Wustholz on Baker inequality      235
XX(N)      127 128
Yau      151
Zagier — Kramarz on rank      28
Zarhin, points in abelian extensions      29
Zarhin, principal polarization      119 121 122
Zarhin, semisimplicity and Tate conjecture      109 112
Zariski topology      3
Zero cycle      31 32 254 255
Zeta function      56 91 93—98 173 260
Zeta function as Eisenstein series      260
Zeta function of abelian variety      91 93—98
Zeta function of elliptic curve      97 98 139—142
Zeta function of Laplace operator      173
Zeta function of number field      56
Zeta function with heights of points      260
Zimmer      72

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