论文标题
偏光K3表面的模量空间的Rapoport-Zink均匀化
Rapoport-Zink uniformization for the moduli space of polarized K3 surfaces
论文作者
论文摘要
我们计算了$ p $ - adig时期图的图像，用于偏光k3表面，并减少了降低。这引起了其模量空间的Rapoport-Zink型均匀化，这是通过局部shimura种类的正交类型的明确开放式刚性分析子变量。与Shimura品种的Rapoport-Zink均匀化相比，与复杂情况类似，统一的域并不具有$ p $ - ad的谎言组的作用，而仅具有离散亚组的作用。我们简要概述如何应用相同的参数来获得平滑立方四倍的模量均匀的均匀化，并减少了超差。
We compute the image of the $p$-adic period map for polarized K3 surfaces with supersingular reduction. This gives rise to a Rapoport-Zink type uniformization of their moduli space by an explicit open rigid analytic subvariety of a local Shimura variety of orthogonal type. In contrast to the case of Rapoport-Zink uniformization of Shimura varieties and in analogy to the complex case, the uniformizing domain does not carry an action of a $p$-adic Lie group, but only of a discrete subgroup. We briefly sketch how the same arguments can be applied to obtain a uniformization for the moduli space of smooth cubic fourfolds with supersingular reduction.
