Large Shafarevich-Tate groups over quadratic number fields

被引：1

作者：

Yu, Myungjun ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

JOURNAL OF NUMBER THEORY | 2019年 / 199卷

关键词：

Elliptic curves; Quadratic twists; Shafarevich-Tate groups; Selmer groups; ELLIPTIC-CURVES;

D O I：

10.1016/j.jnt.2018.12.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E be an elliptic curve over the rational field Q. Let K be a quadratic extension of Q. We show that (under mild conditions on E) for every r > 0, there are infinitely many quadratic twists E-d/Q of E/Q such that dim(F2) (III(E-d/K)[2]) > r. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：98 / 109

页数：12

共 20 条

[1]

[Anonymous], 1986, GRADUATE TEXTS MATH

[2] ORDER OF SAFAREVIC-TATE GROUP CAN BE ARBITRARILY LARGE [J].