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arXiv · 1806.01691

Indivisibility of Heegner points and arithmetic applications

Ashay Burungale·Francesc Castella·Chan-Ho Kim
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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.

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Ashay Burungale, Francesc Castella, Chan-Ho Kim. 2018-06-05. Indivisibility of Heegner points and arithmetic applications. https://arxiv.org/abs/1806.01691

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