2020/09/18 by Patrick Daniels, Daniels, Patrick
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2009.09044
openalex publication_date 2020/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.