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

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. [ABSTRACT FROM AUTHOR]