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

• Autores: Matteo Longo, Víctor Rotger, Carlos de Vera Piquero
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 62, Nº 2, 2018, págs. 355-396
• Idioma: inglés
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• Resumen

  • 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.