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

共 50 条

[1] Elliptic nets and elliptic curves
Stange, Katherine
ALGEBRA & NUMBER THEORY, 2011, 5 (02) : 197 - 229
[2] On the Algebra of elliptic curves
Brzezinski, Tomasz
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2023, 66 (02) : 548 - 556
[3] Ranks of elliptic curves
Rubin, K
Silverberg, A
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 39 (04): : 455 - 474
[4] Elliptic curves and cryptography
Silverman, JH
Public-Key Cryptography, 2005, 62 : 91 - 112
[5] Pairings on elliptic curves
Katholieke Universiteit Leuven, Belgium
Cryptology Inf. Secur. Ser., 2009, (13-30):
[6] LIFTING OF ELLIPTIC CURVES
Gun, Sanoli
Murty, V. Kumar
PACIFIC JOURNAL OF MATHEMATICS, 2019, 301 (01) : 101 - 106
[7] Elliptic curves and cryptography
Jurisic, A
Menezes, AJ
DR DOBBS JOURNAL, 1997, 22 (04): : 26 - +
[8] ELLIPTIC-CURVES
STILLWELL, J
AMERICAN MATHEMATICAL MONTHLY, 1995, 102 (09): : 831 - 837
[9] Algorithms for elliptic curves
Benamara, Oualid
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2022, 25 (02): : 455 - 462
[10] Twists of elliptic curves
Ono, K
COMPOSITIO MATHEMATICA, 1997, 106 (03) : 349 - 360

← 1 2 3 4 5 →