Duke Mathematical Journal

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

Mak Trifković

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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

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

First available in Project Euclid: 10 November 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H52: Elliptic curves [See also 11G05, 11G07, 14Kxx] 14Q05: Curves
Secondary: 11R37: Class field theory 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22]


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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