Special-points conjecture for Shimura varieties

Let $(G,X)$ be a Shimura $p$-datum, let $\operatorname{Sh}_{p}(G,X)$ be its integral model, and let $\mathbb{F}$ be the algebraic closure of the residue field. A point of $\operatorname{Sh}_{p}(G,X)$ with coordinates in $\mathbb{F}$ is a point of the special fibre, and a special point is a point of the Shimura variety in characteristic zero arising from special homomorphisms. Special-points conjecture. Up to isogeny, every point on $\operatorname{Sh}_{p}(G,X)$ with coordinates in $\mathbb{F}$ lifts to a special point on $\operatorname{Sh}_{p}(G,X)$ with coordinates in a finite extension of $B(\mathbb{F})$.

The conjecture is forced by Conjecture LR+ because $\mathcal{L}(G,X)$ contains only terms corresponding to special homomorphisms. The source states that it is proved for simple abelian varieties of PEL type by Zink, and cites announced broader results; thus the unrestricted formulation remains open in the supplied context.