Rational torsion subgroups of modular Jacobian varieties

被引：7

作者：

Ren, Yuan ^{[1
]}

机构：

[1] Sichuan Normal Univ, Sch Math Sci, Chengdu, Sichuan, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2018年 / 190卷

关键词：

Modular curve; Generalized Ogg's conjecture; Eisenstein ideal; FORMS;

D O I：

10.1016/j.jnt.2018.02.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we study the Q-rational torsion subgroups of the Jacobian varieties of modular curves. The main result is that, for any positive integer N, J(0)(N)(Q)(tor)[q(infinity)] = 0 if q is a prime not dividing 6 . N . Pi(p)(vertical bar N)(p(2) - 1). To prove the result, we explicitly construct a collection of Eisenstein series with rational Fourier expansions, and then determine their constant terms to control the size of the rational torsion subgroups. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：169 / 186

页数：18

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