Article contents
Heegner Points over Towers of Kummer Extensions
Published online by Cambridge University Press: 20 November 2018
Abstract
Let $E$ be an elliptic curve, and let
${{L}_{n}}$ be the Kummer extension generated by a primitive
${{p}^{n}}$-th root of unity and a
${{p}^{n}}$-th root of
$a$ for a fixed
$a\,\in \,{{\mathbb{Q}}^{\times }}\,-\,\left\{ \pm 1 \right\}$. A detailed case study by Coates, Fukaya, Kato and Sujatha and
$V$. Dokchitser has led these authors to predict unbounded and strikingly regular growth for the rank of
$E$ over
${{L}_{n}}$ in certain cases. The aim of this note is to explain how some of these predictions might be accounted for by Heegner points arising from a varying collection of Shimura curve parametrisations.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2010
References
- 6
- Cited by