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Darmon's Points and Quaternionic Shimura Varieties

  Published:2011-11-22
 Printed: Dec 2012
  • Jérôme Gärtner,
    Insitut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4 place Jussieu 75005, Paris, France
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Abstract

In this paper, we generalize a conjecture due to Darmon and Logan in an adelic setting. We study the relation between our construction and Kudla's works on cycles on orthogonal Shimura varieties. This relation allows us to conjecture a Gross-Kohnen-Zagier theorem for Darmon's points.
Keywords: elliptic curves, Stark-Heegner points, quaternionic Shimura varieties elliptic curves, Stark-Heegner points, quaternionic Shimura varieties
MSC Classifications: 11G05, 14G35, 11F67, 11G40 show english descriptions Elliptic curves over global fields [See also 14H52]
Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
$L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
11G05 - Elliptic curves over global fields [See also 14H52]
14G35 - Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
11F67 - Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
11G40 - $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
 

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