A Tannakian Framework for G -displays and Rapoport–Zink Spaces

Source abstract

Abstract We develop a Tannakian framework for group-theoretic analogs of displays, originally introduced by Bültel and Pappas, and further studied by Lau. We use this framework to define Rapoport–Zink functors associated to triples $(G,\{\mu \},[b])$, where $G$ is a flat affine group scheme over ${\mathbb{Z}}_p$ and $\mu$ is a cocharacter of $G$ defined over a finite unramified extension of ${\mathbb{Z}}_p$. We prove these functors give a quotient stack presented by Witt vector loop groups, thereby showing our definition generalizes the group-theoretic definition of Rapoport–Zink spaces given by Bültel and Pappas. As an application, we prove a special case of a conjecture of Bültel and Pappas by showing their definition coincides with that of Rapoport and Zink in the case of unramified EL-type local Shimura data.