Diophantine Approximation and Abelian Varieties: Introductory Lectures

Couverture
Springer Science & Business Media, 20 déc. 1993 - 127 pages
The 13 chapters of this book centre around the proof of Theorem 1 of Faltings' paper "Diophantine approximation on abelian varieties", Ann. Math.133 (1991) and together give an approach to the proof that is accessible to Ph.D-level students in number theory and algebraic geometry. Each chapter is based on an instructional lecture given by its author ata special conference for graduate students, on the topic of Faltings' paper.
 

Pages sélectionnées

Table des matières

0017
1
0018
2
0019
3
0020
4
0021
5
0022
6
0023
7
0024
8
0081
65
0082
66
0083
67
0085
69
0086
70
0087
71
0088
72
0089
73

0025
9
0026
10
0027
11
0029
13
0030
14
0031
15
0032
16
0033
17
0034
18
0035
19
0036
20
0037
21
0038
22
0039
23
0040
24
0041
25
0042
26
0043
27
0044
28
0045
29
0046
30
0047
31
0048
32
0049
33
0050
34
0051
35
0052
36
0053
37
0054
38
0055
39
0056
40
0057
41
0058
42
0059
43
0060
44
0061
45
0062
46
0063
47
0064
48
0065
49
0066
50
0067
51
0068
52
0069
53
0070
54
0071
55
0072
56
0073
57
0074
58
0075
59
0076
60
0077
61
0079
62
0080
64
0090
74
0091
75
0092
76
0093
77
0094
78
0095
79
0096
80
0097
81
0098
82
0099
83
0100
84
0101
85
0102
86
0103
87
0104
88
0105
89
0106
90
0107
91
0109
92
0110
94
0111
95
0112
96
0113
97
0114
98
0115
99
0116
100
0117
101
0118
102
0119
103
0120
104
0121
105
0122
106
0123
107
0124
108
0125
109
0126
110
0127
111
0128
112
0129
113
0130
114
0131
115
0132
116
0133
117
0134
118
0135
119
0136
120
0137
121
0138
122
0139
123
0140
124
0141
125
0142
126
0143
127
Droits d'auteur

Autres éditions - Tout afficher

Diophantine Approximation and Abelian Varieties: Introductory Lectures
Bas Edixhoven,Jan-Hendrik Evertse
Aperçu limité - 2009
Diophantine Approximation and Abelian Varieties, Numéro 1566
Bas Edixhoven,J. H. Evertse
Affichage d'extraits - 1993
Diophantine Approximation and Abelian Varieties, Numéro 1566
Bas Edixhoven,J. H. Evertse
Affichage d'extraits - 1993

Expressions et termes fréquents

a₁ abelian subvariety abelian variety affine algebraic number field algebraic variety ample line bundle b₁ C₁ C₂ choose closed subscheme closed subvariety codim(Z coherent sheaf contained d₁ defined definition degree denote dimension dimensional diophantine approximation diophantine equations divisor class elliptic curve exists Faltings Faltings's fibres finite extension finite set finitely many solutions follows global sections h₁ Hence hermitean metric hyperplanes ideal sheaf II(A implies in-k induction inequality intersection number invertible sheaf irreducible component isomorphism linear forms linear subspaces linearly independent Math Mordell's conjecture morphism non-zero norm Note Ox-module points polynomial positive Product Theorem proof of Thm proved rational integer rational numbers result Roth's Lemma Roth's theorem sheaves Siegel's Lemma Sm)d Sp(X space Spec(R subset Subspace theorem subvariety Suppose symmetric trivial tuple upper bound valuations Vojta's conjecture Zariski zero

Références à ce livre

Informations bibliographiques

TitreDiophantine Approximation and Abelian Varieties: Introductory Lectures
Volume 1566 de Lecture Notes in Mathematics
AuteursBas Edixhoven, Jan-Hendrik Evertse
RédacteursBas Edixhoven, Jan-Hendrik Evertse
Éditionillustrée
ÉditeurSpringer Science & Business Media, 1993
ISBN3540575286, 9783540575283
Longueur127 pages
  
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