Proving the triviality of rational points on Atkin-Lehner quotients of Shimura curves

被引：6
作者：
Parent, Pierre
Yafaev, Andrei
机构：
[1] Univ Bordeaux 1, Inst Math & Bordeaux, F-33405 Talence, France
[2] UCL, Dept Math, London WC1E 6BT, England
来源：
MATHEMATISCHE ANNALEN | 2007年 / 339卷 / 04期
基金：
美国国家航空航天局;
关键词：
Singular Point; Modular Form; Rational Point; Abelian Variety; Quaternion Algebra;
D O I：
10.1007/s00208-007-0136-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we give a method for studying global rational points on certain quotients of Shimura curves by Atkin-Lehner involutions. We obtain explicit conditions on such quotients for rational points to be "trivial" (coming from CM points only) and exhibit an explicit infinite family of such quotients satisfying these conditions.
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收藏
页码：915 / 935
页数：21
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