Milne's conjecture on integral canonical models of Shimura varieties

Let $(G_1,\mathcal{X}_1)$ be a Shimura pair such that $G_{1,\mathbb{Q}_p}$ is unramified. Let $H_1$ be a hyperspecial subgroup of $G_1(\mathbb{Q}_p)$, and let $v_1$ be a prime of $E(G_1,\mathcal{X}_1)$ dividing $p$. Write $O_{(v_1)}$ for the local ring at $v_1$. Milne's conjecture. There exists an integral canonical model of $\operatorname{Sh}_{H_1}(G_1,\mathcal{X}_1)$ over $O_{(v_1)}$. This conjecture concerns the existence of good integral models for Shimura varieties at hyperspecial level; it was formulated by Milne as a reformulation of a conjecture of Langlands.