J. Manin. Cyclotomic Fields and Modular Curves. Russian Math. Surveys, 26(6):7--78, 1971. Home/Search Document Not in Database Summary Related Articles Check |
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Non-triviality of families of Heegner points and ranks of.. - Bertolini, Darmon (Correct)
....next proposition does not depend on the assumption that L(E=K; 1) is nonzero. Proposition 2.3 corank p Sel p 1 (E=K1 ) corank p Sel p 1 (E=K) 1. Proof of Proposition 2. 1 The structure theory of discrete modules shows that corank Sel p 1 (E=K1 ) corank p Sel p 1 (E=K1 ) See [M], ch. 1, or also [L] ch. 5, sec. 3, for details. But the propositions 2.2 and 2.3 imply that the p corank of Sel p 1(E=K1 ) is 1. It remains to prove proposition 2.3. Write Kn for the sub eld of K1 having degree p n over K, and Gn for the Galois group Gal(Kn=K) Let Kn0 , with n 0 0 be ....
....n 2 . But the point n2 has in nite order, and therefore it cannot be in nitely divisible in E(Kn2 ) Proof of Proposition 3.1 By corollary 3.3, E(K1 ) p = p has in nite p corank. On the other hand, a cotorsion module has nite p corank, by the structure theory of discrete modules ([M], ch. 1) This completes the proof of proposition 3.1, and of theorem 1.1. The next result gives information on the growth of the Mordell Weil groups E(Kn ) Proposition 3.4 If L(E=K; 1) is non zero, then there is a sequence of integers n having absolute value bounded independently of n such ....
Yu. Manin, Cyclotomic Fields and Modular Curves, Engl. Transl.: Russian Math. Surveys 26 (1971) 7-78.
Invariants des courbes de Frey-Hellegouarch et grands groupes de.. - Nitaj (1998) (1 citation) (Correct)
.... pour d autres r esultats) D autres m ethodes effectives ont et e d evelopp ees par Kramer [19] Mai et Murty [23] pour d eterminer des courbes elliptiques ayant un grand groupe de Tate Shafarevich, mais les premi eres estimations de l ordre de X ont et e conjectur ees par Manin et Lang (voir [24] et [21] Dans cette direction, Goldfeld et Szpiro ( 14] ont propos e la conjecture suivante : Conjecture 1. Pour tout 0, il existe une constante C 1 ( 0 telle que si E=Q est une courbe elliptique de conducteur N et de groupe de Tate Shafarevich X, alors jXj C 1 ( N 1 2 : 1991 ....
Y. Manin, Cyclotomic fields and modular curves, Russian Math. Surveys 26 (1971), 7-78.
Arithmetic of Modular Curves and Applications - Gerhard Frey And (1999) (2 citations) (Correct)
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J. Manin. Cyclotomic Fields and Modular Curves. Russian Math. Surveys, 26(6):7--78, 1971.
Arithmetic of Modular Curves and Applications - Frey, Müller (1998) (2 citations) (Correct)
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J. Manin. Cyclotomic Fields and Modular Curves. Russian Math. Surveys, 26(6):7--78, 1971.
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