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.

引用

页码：513 / 534

页数：22

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