Reductions of an elliptic curve and their Tate-Shafarevich groups

被引：0
作者：
A. C. Cojocaru
W. Duke
机构：
[1] The Fields Institute for Research in Mathematical Sciences,Department of Mathematics
[2] University of California,undefined
来源：
Mathematische Annalen | 2004年 / 329卷
关键词：
Elliptic Curve; Function Field; Reduction Modulo; Positive Proportion; Irrational Point;
D O I：
暂无
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学科分类号：
摘要：
In this paper we study the Tate-Shafarevich groups IIIp of the reductions modulo primes p of an elliptic curve E/ℚ considered as being defined over their function fields. Assuming GRH when E has no CM, we show that IIIp is trivial for a positive proportion of primes p, provided E has an irrational point of order two.
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页码：513 / 534
页数：21
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