Geodesic
Darmon’s Points and Quaternionic Shimura Varieties
Canadian journal of mathematics, Tome 64 (2012) no. 6, pp. 1248-1288

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DOI

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.
DOI : 10.4153/CJM-2011-086-5
Mots-clés : 11G05, 14G35, 11F67, 11G40, elliptic curves, Stark-Heegner points, quaternionic Shimura varieties 
Gärtner, Jérôme. Darmon’s Points and Quaternionic Shimura Varieties. Canadian journal of mathematics, Tome 64 (2012) no. 6, pp. 1248-1288. doi: 10.4153/CJM-2011-086-5
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     title = {Darmon{\textquoteright}s {Points} and {Quaternionic} {Shimura} {Varieties}},
     journal = {Canadian journal of mathematics},
     pages = {1248--1288},
     year = {2012},
     volume = {64},
     number = {6},
     doi = {10.4153/CJM-2011-086-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-086-5/}
}
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