Darmon's points and quaternionic Shimura varieties

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.

30 pages

Cited by in corpus (2)

• Computation of ATR Darmon points on non-geometrically modular elliptic curves
• Almost totally complex points on elliptic curves