Reductions of an elliptic curve and their Tate-Shafarevich groups

被引：12
|
作者：
Cojocaru, AC
Duke, W
机构：
[1] Fields Inst Res Math Sci, Toronto, ON M5T 3J1, Canada
[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA
来源：
MATHEMATISCHE ANNALEN | 2004年 / 329卷 / 03期
关键词：
D O I：
10.1007/s00208-004-0517-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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：22
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