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.
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页码：4976 / 4993
页数：18
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