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| Ïîèñê ïî óêàçàòåëÿì |
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| Serre J.-P. — Lectures on the Mordell-Weil Theorem |
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| Ïðåäìåòíûé óêàçàòåëü |
Number of torsion points of bounded degree on an abelian variety 44
Order of a ring of integers 191
Order of a ring of integers conductor of an order 191
P(n), the greatest prime factor of n 105—106
p-adic methods 60 67
p-adic methods Chabauty’s theorem 58—60
Partition of unity 84
Pell — Fermat equation  4 94 136
Picard group Pic(X) 2 20—22 34—36 157
Picard group Pic(X), Pic°(X) 25 31
Poincare divisor class 37 76 78
Poincare upper half plane 67—68 71
Pontrjagin dual 164
Prime number theorem 181
Principal homogeneous space 100
Product formula, for a family of absolute values 7-10 22
Product formula, for a family of absolute values function fields 7—8
Product formula, for a family of absolute values number fields 7—10 113
Profinite group 147—149
Profinite group Frattini subgroup 148—149
Puiseux expansion 130—131 198
Pure transcendental extension 147 154 159
Quadratic functors on projective varieties 34
Quadraticity of heights on abelian varieties 35—39 42
Quadraticity of heights on abelian varieties on elliptic curves 40—41
Quasi-integral set of points 4—6 94
Rank of Mordell — Weil group 3 52 63 66 69 80 152 154—162
Rank of Mordell — Weil group elliptic curves over  of large rank 154—162
Rank of Mordell — Weil group Honda’s conjecture 162
Rank of Mordell — Weil group is effectively bounded 52
Regular field extension 137
Restriction of scalars functor 128
Riemann hypothesis 188
Riemann — Roch theorem 74 109
Riemann’s existence theorem 141
S-integers 102—105 112 134—136 141
S-units 103 112
Schanuel’s theorem 17—19 27—28 132 178
Selberg’s bound, for the large sieve 171—172
Sextic resolvent 125
Shih’s theorem 146—147
Siegel’s theorem 4—5 94—95 101—105 116 134 136 163
Siegel’s theorem application to curves of genus  1 101—102
Siegel’s theorem application to P(f(n)) 105—106
| Siegel’s theorem approximation theorem on an abelian variety 98—101
Siegel’s theorem effectivity 5 100—101 106—107 116
Siegel’s theorem exceptional curve see “Exceptional curve”
Siegel’s theorem the case of curves of genus 0 102—104
Siegel’s theorem Thue — Siegel — Roth theorem 4 95—100 104—105 107
Sieve, the large 5—6 163—176
Sigma function of Weierstrass 91
Silverman’s theorem 154
Specialisation of Galois groups 122—126 137—138
Specialisation of Mordell — Weil groups, Neron’s theorem 59 152—154
Stark’s conjectures 199
Strongly continuous functions 83
Superelliptic curve 117
Swan’s example 147
Sylow subgroup 124 147—148
Tate curve 91
Tate module of an abelian variety 70 119
Tate’s normalisation lemma 29—30
Tate’s recipe for local heights 91—93
Tauberian theorem 44 183
Theta functions (and local heights) 88—89 91
Thin set of points 121 (see also “Hilbert’s irreducibility theorem”)
Thin set of points Cohen’s theorem 6 177—178
Thin set of points extension of ground field 128—129
Thin set of points in  , upper bounds 5—6 132—136
Thin set of points in  , upper bounds 6 177—178
Thin set of points intersected with plane sections 127—128
Thin set of points of type 1 121
Thin set of points of type 2 121
Thin set of points polynomial interpretation 122
Thin set of points reduction modulo p of a thin set 179—180 183—186
Thue — Siegel — Roth theorem 4 95—100 104—105 107
Thue — Siegel — Roth theorem approximation of real numbers 95—97
Thue — Siegel — Roth theorem for function fields 105
Thue’s equation 114
Torsion points of bounded degree on an abelian variety 44
Torsion subgroup, of the Mordell — Weil group 43—44 53—54 68
Torsion subgroup, of the Mordell — Weil group number of torsion points 44 69
Weak Mordell — Weil theorem 3 51—52 99
Weak Mordell — Weil theorem explicit form 55—57
Weak Mordell — Weil theorem non-abelian generalisation 52
Weak Mordell — Weil theorem via Galois cohomology 51—52
Weierstrass embedding of an elliptic curve 40 57 90 115 119 155
X(N) 118 193
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