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.
Citation
Matteo Longo. Víctor Rotger. Carlos de Vera-Piquero. "Heegner points on Hijikata–Pizer–Shemanske curves and the Birch and Swinnerton-Dyer conjecture." Publ. Mat. 62 (2) 355 - 396, 2018. https://doi.org/10.5565/PUBLMAT6221803
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