Indivisibility of Heegner points and arithmetic applications
Number Theory
2018-08-23 v2
Abstract
We upgrade Howard's divisibility towards Perrin-Riou's Heegner point main conjecture to the predicted equality. Contrary to previous works in this direction, our main result allows for the classical Heegner hypothesis and non-squarefree conductors. The main ingredients we exploit are W.~Zhang's proof of Kolyvagin's conjecture, Kolyvagin's structure theorem for Shafarevich--Tate groups, and the explicit reciprocity law for Heegner points.
Cite
@article{arxiv.1806.01691,
title = {Indivisibility of Heegner points and arithmetic applications},
author = {Ashay Burungale and Francesc Castella and Chan-Ho Kim},
journal= {arXiv preprint arXiv:1806.01691},
year = {2018}
}