A duality theorem for Dieudonne displays

剪切显示与$p$-可除群

Sheared displays and $p$-divisible groups

利用剪切Witt向量为$p$-可除群建立Dieudonné理论。

Smoothness of the truncated display functor

We show that to every p-divisible group over a p-adic ring one can associate a display by crystalline Dieudonne theory. For an appropriate notion of truncated displays, this induces a functor from truncated Barsotti-Tate groups to truncated displays, which is a smooth morphism of smooth algebraic stacks. As an application we obtain a new proof of the equivalence between infinitesimal p-divisible groups and nilpotent displays over p-adic rings, and a new proof of the equivalence due to Berthelot and Gabber between commutative finite flat group schemes of p-power order and Dieudonne modules over…

拟合成环上棱柱高阶 $(G,\mu)$-显示形的形变

Deformations of Prismatic Higher $(G,μ)$-Displays over Quasi-Syntomic Rings

本文证明了拟合成环上棱柱高阶 $(G,\mu)$-显示形的形变定理，并据此推广了 $p$-可除群的棱柱 Dieudonné 模分类，且将该显示形叠与积分局部 Shimura 簇相关联。

2-adic integral canonical models and the Tate conjecture in characteristic 2

We use E. Lau's classification of 2-divisible groups using Dieudonné displays to construct integral canonical models for Shimura varieties of abelian type at 2-adic places where the level is hyperspecial. We apply this to prove the Tate conjecture for K3 surfaces in characteristic 2.

$G$-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 ass…

The classification of $p$-divisible groups over 2-adic discrete valuation rings

Let $\mathscr{O}_K$ be a 2-adic discrete valuation ring with perfect residue field $k$. We classify $p$-divisible groups and $p$-power order finite flat group schemes over $\mathscr{O}_K$ in terms of certain Frobenius module over $\mathfrak{S}:=W(k)[[u]]$. We also show the compatibility with crystalline Dieudonné theory and associated Galois representations. Our approach differs from Lau's generalization of display theory, and we additionally obtain the the compatibility with associated Galois representations.