Heuristics on Tate-Shafarevitch Groups of Elliptic Curves Defined over Q
Heuristics on Tate-Shafarevitch Groups of Elliptic Curves Defined over Q
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Q 上定义的椭圆曲线 Tate-Shafarevitch 群的启发法
作者：
C. Delaunay
在一个著名的文件中，科恩和Lenstra给出了代数的阶级群体的一些领域。本文给出了定义在Q上的椭圆曲线的Tate-Shafarevitch群的类似结果。对于这样的群（如果它们是有限的），存在一个非退化的交替双线性对。我们给出此类群的一些性质，然后制定启发式方法，使我们能够给出精确的猜想。
In a well-known paper, Cohen and Lenstra gave conjectures on class groups of number fields. We give here similar conjectures for Tate-Shafarevitch groups of elliptic curves defined over Q. For such groups (if they are finite), there exists a nondegenerate, alternating, bilinear pairing. We give some properties of such groups and then formulate heuristics which allow us to give precise conjectures.