Heegner Points over Towers of Kummer Extensions
نویسندگان
چکیده
Let E be an elliptic curve, and let Ln be the Kummer extension generated by a primitive pnth root of unity and a pn-th root of a for a fixed a ∈ Q − {±1}. 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 Ln 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.
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