Regulators of Elliptic Curves

被引：3

作者：

Autissier, Pascal ^{[1
]}

Hindry, Marc ^{[2
]}

Pazuki, Fabien ^{[3
]}

机构：

[1] Univ Bordeaux, Inst Math Bordeaux, 351 Cours Liberat, F-33405 Talence, France

[2] Univ Paris Diderot, Inst Math Jussieu Paris Rive Gauche, UFR Math, Batiment Sophie Germain,Rue Thomas Mann, F-75013 Paris, France

[3] Univ Copenhagen, Dept Math Sci, Univ Pk 5, DK-2100 Copenhagen O, Denmark

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2021年 / 2021卷 / 07期

基金：

新加坡国家研究基金会;

关键词：

ABELIAN-VARIETIES; POINTS; HEIGHT; RANK;

D O I：

10.1093/imrn/rny285

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the regulator of the Mordell-Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic p > 0. We prove a new Northcott property for the regulator of elliptic curves of rank at least 4 defined over a number field. In the function field case, we obtain that non-trivial families of elliptic curves with bounded regulators and bounded ranks are limited families. We conclude by asking new questions.

引用

页码：4976 / 4993

页数：18

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