Darmon's Stark–Heegner point conjecture

Let $f$ be a weight-$2$ newform of level $\Gamma_0(p)$ with integer Fourier coefficients, let $E=E_f$ be the associated elliptic curve with multiplicative reduction at $p$, and let $P_\tau^{\pm}$ be the Stark–Heegner point obtained from the elliptic theta cocycles and Tate uniformisation. Let $\tau\in\Gamma\backslash\mathcal{H}_p^{\operatorname{RM}}$ be a point of discriminant $D$ prime to $p$, and let $H_\tau$ be the narrow ring class field of the order $\mathcal{O}_\tau$ attached to $\tau$. Darmon's Stark–Heegner point conjecture. One has

$$P_\tau^{\pm}\in E(H_\tau).$$

This conjecture is the real-quadratic analogue of the algebraicity of classical Heegner points and predicts that the $p$-adicly constructed points are defined over the corresponding narrow ring class fields. The source states that it and suitable generalisations have been verified extensively.