Duke Mathematical Journal
- Duke Math. J.
- Volume 135, Number 3 (2006), 415-453.
Stark-Heegner points on elliptic curves defined over imaginary quadratic fields
Let be an elliptic curve defined over an imaginary quadratic field of class number . No systematic construction of global points on such an is known. In this article, we present a -adic analytic construction of points on , which we conjecture to be global, defined over ring class fields of a suitable relative quadratic extension . 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
Duke Math. J., Volume 135, Number 3 (2006), 415-453.
First available in Project Euclid: 10 November 2006
Permanent link to this document
Digital Object Identifier
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