Rapoport's surjectivity conjecture for Newton strata of parahoric Shimura varieties

Let $Sh_{K_p}$ be a PEL Shimura variety with standard parahoric level subgroup $K_p$, and let

$$\delta_{K_p}:Sh_{K_p}(k)\longrightarrow B(G,\mu)$$

be the map sending a point to the $c3$-conjugacy class of its associated isocrystal. The fibers of this map are the Newton strata, and the basic locus is the inverse image of $B(G,\mu)\cap B(G)_{basic}$. Rapoport's conjecture. The map

$$\delta_{K_p}:Sh_{K_p}(k)\longrightarrow B(G,\mu)$$

is surjective. In particular, the basic locus is nonempty. This asserts that every admissible Newton stratum occurs on the special fiber of the Shimura variety. The surrounding discussion identifies this as a fundamental conjecture; no resolution is supplied here.