Resumen de Heegner points on Hijikata–Pizer–Shemanske curves and the Birch and Swinnerton-Dyer conjecture
Matteo Longo, Víctor Rotger, Carlos de Vera Piquero
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.
