Heegner points on Hijikata-Pizer-Shemanske curves
Number Theory
2016-03-14 v1
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.
Keywords
Cite
@article{arxiv.1603.03554,
title = {Heegner points on Hijikata-Pizer-Shemanske curves},
author = {Matteo Longo and Victor Rotger and Carlos de Vera-Piquero},
journal= {arXiv preprint arXiv:1603.03554},
year = {2016}
}