论文标题
$ g $ - 霍奇类型和正式$ p $ - 可分别的群体
$G$-displays of Hodge type and formal $p$-divisible groups
论文作者
论文摘要
让$ g $是$ p $ - 亚法整数的还原集团计划，让$μ$成为$ g $的微小共同体。在Hodge型案例中，我们从nilpotent $（g，μ）$中构建了一个函数 - 超过$ p $ - nilpotent rings $ r $ r $ to正式$ p $ p $ p $ r $，配备了$ r $，配备有结晶的潮汐量。当$ r/pr $在本地具有$ p $ basisétale时，我们表明这定义了这两个类别之间的等价性。函子的定义依赖于与任何与nilpotent $（g，μ）$ - 显示相关的$ g $ crystal的构建，这扩展了与nilpotent Zink显示器相关的DieudonnéCrystal的构造。作为应用程序，我们获得了Kim和Bültel和Pappas所定义的Hodge类型的Rapoport-Zink函子之间的明确比较。
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.
