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Darmon’s Points and Quaternionic Shimura Varieties

Published online by Cambridge University Press:  20 November 2018

Jérôme Gärtner
Jérôme Gärtner*
Affiliation:
Insitut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4 place Jussieu 75005, Paris, France email: jgartner@math.jussieu.fr
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Abstract

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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

11G0514G3511F6711G40elliptic curvesStark-Heegner pointsquaternionic Shimura varieties

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 6 , 01 December 2012 , pp. 1248 - 1288
Copyright
Copyright © Canadian Mathematical Society 2012

References

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