Abstract

We give a description of the $\textrm{GL}_4$ Rapoport–Zink space, including the connected components, irreducible components, intersection behavior of the irreducible components, and Ekedahl–Oort stratification. As an application of this, we also give a description of the supersingular locus of the Shimura variety for the group $\textrm{GU}(2,2)$ over a prime split in the relevant imaginary quadratic field.

中文翻译：

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GL4 Rapoport–Zink Space

摘要

我们给出了 $\textrm{GL}_4$ Rapoport-Zink 空间的描述，包括连通分量、不可约分量、不可约分量的交集行为和 Ekedahl-Oort 分层。作为对此的应用，我们还描述了组 $\textrm{GU}(2,2)$ 在相关假想二次域中的素数分裂上的 Shimura 变体的超奇异轨迹。