Three-descent and the Birch and Swinnerton-Dyer conjecture

被引：7

作者：

Bandini, A ^{[1
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2004年 / 34卷 / 01期

关键词：

D O I：

10.1216/rmjm/1181069889

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a three-descent procedure to bound and, in some cases, compute the three-part of the Selmer and Tate-Shafarevich group of the curves y(2) = x(3) + a, a a nonzero integer. This enables us to verify the whole Birch and Swinnerton-Dyer conjecture for some of such curves.

引用

页码：13 / 27

页数：15

共 17 条

[1]

BIRCH BJ, 1965, J REINE ANGEW MATH, V218, P79

[2]

Cassels JWS, 1998, J REINE ANGEW MATH, V494, P101

[3] CONJECTURE OF BIRCH AND SWINNERTON-DYER [J].