Pappas–Rapoport conjecture on canonical integral models of parahoric Shimura varieties

Let $(\mathcal{G},\mathbf{G},\mathbf{X})$ be a parahoric Shimura datum, and let $\{\operatorname{Sh}_{\sf K}(\mathbf{G},\mathbf{X})\}_{{\sf K}^p}$ denote the associated system of Shimura varieties indexed by prime-to-$p$ level subgroups. An canonical integral model is an integral model of this system with the canonical properties considered in the paper. Pappas–Rapoport conjecture. For any parahoric Shimura datum $(\mathcal{G},\mathbf{G},\mathbf{X})$, there exists an canonical integral model for $\{\operatorname{Sh}_{\sf K}(\mathbf{G},\mathbf{X})\}_{{\sf K}^p}$. The conjecture asserts existence; the preceding uniqueness result shows that such a system, together with the associated shtukas, is unique up to unique isomorphism if it exists. The paper studies canonical integral models of Shimura varieties of abelian type.