ON THE MORDELL-WEIL AND SHAFAREVICH-TATE GROUPS FOR WEIL ELLIPTIC CURVES
ON THE MORDELL-WEIL AND SHAFAREVICH-TATE GROUPS FOR WEIL ELLIPTIC CURVES
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论Weil椭圆曲线的Mordell-Weil群和Shafarevich-Tate群
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
V. Kolyvagin
中科院分区：
文献类型：
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作者：
V. Kolyvagin
让？是一个？椭圆曲线在场上的位置？有理数的函数，，在哪里？是at的零的数量级。让？是与判别式，Heegner点，或非平凡形式的虚二次扩展？结束了吗根据或？证明了如果？有无穷阶（如果是这样，那么群和被a湮没？正整数？(in（1）群是有限的，由？当它被证明，符合的约束有限阶的一些？以.它也证明了是平凡的？23椭圆曲线。书目：21种。
Let? be a?Weil elliptic curve over the field? of rational numbers, the -function over?, , where? is the order of the zero of at . Let? be the imaginary quadratic extension of with discriminant , the Heegner point, or the nontrivial form of? over? according as or?. It is proved that if? has infinite order (which is so if , , then the groups and are annihilated by a?positive integer? (in particular the groups are finite) determined by?. When it is proved that coincides with the conjectured finite order of for some? with . It is also proved that is trivial for?23 elliptic curves. Bibliography: 21 titles.