Duke Mathematical Journal

Stark-Heegner points on elliptic curves defined over imaginary quadratic fields

Mak Trifković

Abstract

Let $E$ be an elliptic curve defined over an imaginary quadratic field $F$ of class number $1$. No systematic construction of global points on such an $E$ is known. In this article, we present a $p$-adic analytic construction of points on $E$, which we conjecture to be global, defined over ring class fields of a suitable relative quadratic extension $K/F$. The construction follows ideas of Darmon to produce an analog of Heegner points, which is especially interesting since none of the geometry of modular parametrizations extends to this setting. We present some computational evidence for our construction

Article information

Source
Duke Math. J., Volume 135, Number 3 (2006), 415-453.

Dates
First available in Project Euclid: 10 November 2006

https://projecteuclid.org/euclid.dmj/1163170198

Digital Object Identifier
doi:10.1215/S0012-7094-06-13531-7

Mathematical Reviews number (MathSciNet)
MR2272972

Zentralblatt MATH identifier
1111.14025

Citation

Trifković, Mak. Stark-Heegner points on elliptic curves defined over imaginary quadratic fields. Duke Math. J. 135 (2006), no. 3, 415--453. doi:10.1215/S0012-7094-06-13531-7. https://projecteuclid.org/euclid.dmj/1163170198

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