Darmon’s points and quaternionic Shimura varieties. (English) Zbl 1305.11051
Summary: We generalize a conjecture due to H. Darmon and A. Logan [Int. Math. Res. Not. 2003, No. 40, 2153–2180 (2003; Zbl 1038.11035)] 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.
MSC:
| 11G05 | Elliptic curves over global fields |
| 14G35 | Modular and Shimura varieties |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11G40 | \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture |
