Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jul 2018 Italy, Spain English Publisher:Universitat Autonoma de BarcelonaJournal:Publicacions Matemàtiques, volume 62, pages 355-396 (issn: 0214-1493,

Copyright policy )Funded by:EC | BSD

Authors: Matteo Longo; Víctor Rotger; Carlos de Vera-Piquero;

doi: 10.5565/publmat6221803

handle: 2117/123220 , 11577/3281245

Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture

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Abstract

We study Heegner points on elliptic curves, or more generally modular abelian varieties, coming from uniformization by Shimura curves attached to a rather general type of quaternionic orders. We address several questions arising from the Birch and Swinnerton-Dyer (BSD) conjecture in this general context. In particular, under mild technical conditions, we show the existence of non-torsion Heegner points on elliptic curves in all situations in which the BSD conjecture predicts their existence. Peer Reviewed

Countries

Italy, Spain

Related Organizations

Universitat Politècnica de Catalunya
Spain
University of Padua
Italy
Universitat Polite`cnica de Catalunya
Spain
Autonomous University of Barcelona
Spain
University of Zaragoza
Spain

Keywords

11G40, Shimura curves, Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry), 510, Geometria algèbrica--Aritmètica, BSD conjecture; Heegner points; L-functions; Shimura curves;, L-functions, BSD conjecture; Heegner points; L-functions; Shimura curves, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica, Mathematik, Heegner points, :11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) [Classificació AMS], :Matemàtiques i estadística::Anàlisi matemàtica [Àrees temàtiques de la UPC], $L$-functions, Arithmetical algebraic geometry, 11G05, 11G18, BSD conjecture

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