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arXiv · 1603.03554

Heegner points on Hijikata-Pizer-Shemanske curves

Matteo Longo·Victor Rotger·Carlos de Vera-Piquero
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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 or- ders closely related to those introduced by Hijikata{Pizer{Shemanske in the 80's. We address several questions arising from the Birch and Swinnerton-Dyer (BSD) conjecture in this general context. In par- ticular, 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.

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Matteo Longo, Victor Rotger, Carlos de Vera-Piquero. 2016-03-11. Heegner points on Hijikata-Pizer-Shemanske curves. https://arxiv.org/abs/1603.03554

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