Darmon's points and quaternionic Shimura varieties

Jerome Gartner (1)

1 IMJ - Institut de Mathématiques de Jussieu

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.

Mots clés: quaternionic Shimura varieties; Elliptic curves; Stark-Heegner points; quaternionic Shimura varieties.

Domaines: Théorie des nombres [math.NT]

Jerome Gartner. Darmon's points and quaternionic Shimura varieties. 2011. ⟨hal-00586532⟩