Geodesic
Heegner Points over Towers of Kummer Extensions
Canadian journal of mathematics, Tome 62 (2010) no. 5, pp. 1060-1081

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DOI

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.
DOI : 10.4153/CJM-2010-039-8
Mots-clés : 11G05, 11R23, 11F46 
Darmon, Henri; Tian, Ye. Heegner Points over Towers of Kummer Extensions. Canadian journal of mathematics, Tome 62 (2010) no. 5, pp. 1060-1081. doi: 10.4153/CJM-2010-039-8
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     title = {Heegner {Points} over {Towers} of {Kummer} {Extensions}},
     journal = {Canadian journal of mathematics},
     pages = {1060--1081},
     year = {2010},
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     doi = {10.4153/CJM-2010-039-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-039-8/}
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