# Integration on $\mathcal{H}_p \times \mathcal{H}$ and arithmetic applications

### Abstract

This article describes a conjectural $p$-adic analytic construction of global points on (modular) elliptic curves, points which are defined over the ring class fields of real quadratic fields. The resulting conjectures suggest that the classical Heegner point construction, and the theory of complex multiplication on which it is based, should extend to a variety of contexts in which the underlying field is not a CM field.

Henri Darmon