Equations of hyperelliptic Shimura curves

被引：9
|
作者：
Molina, Santiago [1 ]
机构：
[1] Univ Politecn Cataluna, Dept Matemat Aplicada EPSVG 4, Vilanova I La Geltru 08800, Spain
来源：
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2012年 / 105卷
关键词：
POINTS; GENUS;
D O I：
10.1112/plms/pds020
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe a method for computing equations of hyperelliptic Shimura curves attached to indefinite quaternion algebras over Q and Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld's non-archimedean uniformization of Shimura curves, a formula of Gross and Zagier for the endomorphism ring of Heegner points over Artinian rings and the connection between Ribet's bimodules and the specialization of Heegner points, as introduced in Molina ['Ribet bimodules and specialization of Heegner points', Israel Journal of Mathematics]. We provide a list of equations of Shimura curves and quotients of them obtained by our method that had been conjectured by Kurihara.
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页码：891 / 920
页数：30
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