The non-emptiness conjecture for parahoric Rapoport–Zink spaces

Let $\mathcal{D}_{\mathbb{Z}_p}$ be an integral Rapoport–Zink datum such that $[b]\in B(G,\{\mu\})$, and suppose that the group scheme $\mathcal{G}$ is parahoric. Non-emptiness conjecture. The rigid-analytic space over $\breve E$ associated to the formal scheme $\mathcal{M}_{\mathcal{D}_{\mathbb{Z}_p}}$ is non-empty. This is proposed as the converse of the preceding non-emptiness criterion and would provide a partial answer to the paper’s question about when the Rapoport–Zink space is non-empty.