An analogue for elliptic curves of the Grunwald-Wang example

被引：21

作者：

Dvornicich, R

Zannier, U

机构：

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

[2] Inst Univ Architettura DCA, I-30135 Venice, Italy

来源：

COMPTES RENDUS MATHEMATIQUE | 2004年 / 338卷 / 01期

关键词：

D O I：

10.1016/j.crma.2003.10.034

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give examples of elliptic curves epsilon/Q and rational points P is an element of epsilon(Q) such that P is divisible by 4 in epsilon(Q(v)) for each rational place v but P is not divisible by 4 in epsilon(Q). This is an analogue of a well-known example, with G(m) in place of epsilon: namely, P = 16 is a rational 8-th power locally almost everywhere, but not globally in Q* = G(m)(Q). (C) 2003 Academie des sciences. Published by Elsevier SAS. All rights reserved.

引用

页码：47 / 50

页数：4

共 6 条

[1]

Artin E., 1967, Class field theory

[2] Local-global divisibility of rational points in some commutative algebraic groups [J].