G-displays of Hodge type and formal p-divisible groups

Let G be a reductive group scheme over the p -adic integers, and let μ be a minuscule cocharacter for G . In the Hodge-type case, we construct a functor from nilpotent ( G , μ ) -displays over p -nilpotent rings R to formal p -divisible groups over R equipped with crystalline Tate tensors. When R / pR has a p -basis étale locally, we show that this defines an equivalence between the two categories. The definition of the functor relies on the construction of a G -crystal associated with any adjoint nilpotent ( G , μ ) -display, which extends the construction of the Dieudonné crystal associated with a nilpotent Zink display. As an application, we obtain an explicit comparison between the Rapoport-Zink functors of Hodge type defined by Kim and by Bültel and Pappas.