Serre J.-P. — Lectures on the Mordell-Weil Theorem :: Электронная библиотека попечительского совета мехмата МГУ

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Serre J.-P. — Lectures on the Mordell-Weil Theorem

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Название: Lectures on the Mordell-Weil Theorem

Автор: Serre J.-P.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3-d

Год издания: 1997

Количество страниц: 218

Добавлена в каталог: 21.06.2006

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Предметный указатель

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 $\mathbf{Q}$ 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 $\geq$ 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 $\mathbf{P}_1$ , upper bounds      5—6 132—136
Thin set of points in $\mathbf{P}_n$ , 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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