Global Divisibility of Heegner Points and Tamagawa Numbers
نویسنده
چکیده
We improve Kolyvagin’s upper bound on the order of the p-primary part of the Shafarevich-Tate group of an elliptic curve of rank one over a quadratic imaginary field. In many cases, our bound is precisely the one predicted by the Birch and Swinnerton-Dyer conjectural formula.
منابع مشابه
Heegner Point Kolyvagin System and Iwasawa Main Conjecture
In this paper we prove an anticyclotomic Iwasawa main conjecture proposed by PerrinRiou for Heegner points when the global sign is −1, using a recent work of the author on one divisibility of Iwasawa-Greenberg main conjecture for Rankin-Selberg p-adic L-functions. As a byproduct we also prove the equality for the above mentioned main conjecture under some local conditions, and an improvement of...
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Let E be an optimal elliptic curve over Q of conductor N , such that the L-function of E vanishes to order one at s = 1. Let K be a quadratic imaginary field in which all the primes dividing N are split and such that the L-function of E over K also vanishes to order one at s = 1. In view of the Gross-Zagier theorem, the Birch and Swinnerton-Dyer conjecture says that the index in E(K) of the sub...
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