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arXiv · 1807.09997

The basic locus of the unitary Shimura variety with parahoric level structure, and special cycles

Sungyoon Cho
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Abstract

In this paper, we study the basic locus in the fiber at $p$ of a certain unitary Shimura variety with a certain parahoric level structure. The basic locus $\widehat{\mathcal{M}^{ss}}$ is uniformized by a formal scheme $\mathcal{N}$ which is called Rapoport-Zink space. We show that the irreducible components of the induced reduced subscheme $\mathcal{N}_{red}$ of $\mathcal{N}$ are Deligne-Lusztig varieties and their intersection behavior is controlled by a certain Bruhat-Tits building. Also, we define special cycles in $\mathcal{N}$ and study their intersection multiplicities.

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Sungyoon Cho. 2018-07-26. The basic locus of the unitary Shimura variety with parahoric level structure, and special cycles. https://arxiv.org/abs/1807.09997

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