OGG'S TORSION CONJECTURE: FIFTY YEARS LATER

被引：0

作者：

Balakrishnan, Jennifer S. ^{[1
]}

Mazur, Barry ^{[2
]}

机构：

[1] Boston Univ, Dept Math & Stat, Boston, MA 02215 USA

[2] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2025年 / 62卷 / 02期

关键词：

ELLIPTIC-CURVES; RATIONAL-POINTS; QUADRATIC CHABAUTY; ABELIAN-VARIETIES; EISENSTEIN IDEALS; FUNDAMENTAL GROUP; SUBGROUPS; THEOREM; BOUNDS; UNIFORMITY;

D O I：

10.1090/bull/1851

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Andrew Ogg's mathematical viewpoint has inspired an increasingly broad array of results and conjectures. His results and conjectures have earmarked fruitful turning points in our subject, and his influence has been such a gift to all of us. Ogg's celebrated torsion conjecture-as it relates to modular curves-can be paraphrased as saying that rational points (on the modular curves that parametrize torsion points on elliptic curves) exist if and only if there is a good geometric reason for them to exist. We give a survey of Ogg's torsion conjecture and the subsequent developments in our understanding of rational points on modular curves over the last fifty years.

引用

页码：235 / 268

页数：34

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