Bounds for the order of the Tate-Shafarevich group
Bounds for the order of the Tate-Shafarevich group
复制标题
Tate-Shafarevich 群阶的界限
DOI：
--
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
L. Szpiro
中科院分区：
文献类型：
--
作者：
D. Goldfeld;L. Szpiro
在本文中，我们证明了，在Q上，与经典的代数，如Birch和Swinnerton-Dyer，之间的等价性模椭圆曲线以下两个代数：有关阶1 ID的Tate-Shafarevich群，导体N和判别式D的椭圆曲线。对于函数域，我们也证明了（1）成立，因为（2）已经被我们中的一个人证明了。
In this paper we show, over Q, with classical conjectures like Birch and Swinnerton-Dyer, the equivalence for modular elliptic curves between the following two conjectures: relating the order 1 ID of the Tate-Shafarevich group, the conductor N and the discriminant D of an elliptic curve. We also show for function fields that (1) stands because (2) has been proved earlier by one of us.