Torsion bounds for elliptic curves and Drinfeld modules

被引：17

作者：

Breuer, Florian ^{[1
]}

机构：

[1] Univ Stellenbosch, Dept Math Sci, ZA-7600 Stellenbosch, South Africa

来源：

JOURNAL OF NUMBER THEORY | 2010年 / 130卷 / 05期

关键词：

Elliptic curves; Drinfeld modules; Torsion points; Galois representations; ABELIAN-VARIETIES; POINTS; NUMBER;

D O I：

10.1016/j.jnt.2009.11.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive upper bounds on the number of L-rational torsion points on a given elliptic curve or Drinfeld module defined over a finitely generated field K. as a function of the degree [L: K]. Our main tool is the adobe openness of the image of Galois representations, due to Serre, Pink and Rutsche. Our approach is to prove a general result for certain Galois modules, which applies simultaneously to elliptic curves and to Drinfeld modules. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1241 / 1250

页数：10

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