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

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Title:	Heegner points on Hijikata- Pizer- Shemanske curves and the Birch and Swinnerton-Dyer conjecture
Author:	Longo, Matteo; Rotger, Víctor; de Vera-Piquero, Carlos
Abstract:	We study Heegner points on elliptic curves, or more generally modular abelian varieties, coming from uniformization by Shimura curves attached to a rathergeneral 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.
Subject(s):	-BSD conjecture -Heegner points -L-functions -Shimura curves
Rights:	open access Tots els drets reservats. https://rightsstatements.org/vocab/InC/1.0/
Document type:	Article
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Uri:	https://ddd.uab.cat/record/191237