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

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 cont...

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Detalles Bibliográficos
Autores: Longo, Matteo, Rotger, Víctor, de Vera-Piquero, Carlos
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:191237
Acceso en línea:https://ddd.uab.cat/record/191237
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6221803
Access Level:acceso abierto
Palabra clave:BSD conjecture
Heegner points
L-functions
Shimura curves
Descripción
Sumario: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.