Moduli of generalised displays and period maps

几何对象的模和线性结构空间的周期映射在几何和算术中起着核心作用。正特征周期映射的一个主要来源是代数簇的结晶上同调的附加结构。在这个项目中，我们希望专注于展示结构。作为一个出发点，我们认为，从截断Barsotti-Tate组的空间到截断（标准）显示器的空间的周期图。我们问有多少信息可以恢复从这个地图。此外，我们想发展一个理论的截断G-显示的线性代数群G，研究这些对象的模空间，并定义和研究周期态射到这些空间。我们期望应用于例如PEL Shimura品种的还原和K3表面。

Moduli of geometric objects and period maps into spaces of linear structures play a central role in geometry and arithmetic. A main source of period maps in positive characteristic is given by additional structures on the crystalline cohomology of algebraic varieties. In this project we want to focus on display structures. As a starting point we consider the period map from the space of truncated Barsotti-Tate groups into the space of truncated (standard) displays. We ask how much information can be recovered from this map. Moreover, we want to develop a theory of truncated G-displays for a linear algebraic group G, study the moduli spaces of these objects, and define and study period morphisms into these spaces. We expect applications for example to reductions of PEL Shimura varieties and to K3 surfaces.