Irreducibility of the Hilbert-Blumenthal moduli spaces with parahoric level structure

Irreducibility of the Siegel moduli spaces with parahoric level structure

We prove that the moduli space ${\mathcal A}_{g,Γ_0(p)}\otimes \bar {\mathbb F}_p$ of principally polarized abelian varieties of dimension $g$ with a $Γ_0(p)$-level structure in characteristic $p$ has $2^g$ irreducible components.The cases of other parahoric level structures are also considered.

Irreducibility and p-adic monodromies on the Siegel moduli spaces

We generalize the surjectivity result of the $p$-adic monodromy for the ordinary locus of a Siegel moduli space by Faltings and Chai (independently by Ekedahl) to that for any $p$-rank stratum. We discuss irreducibility and connectedness of some $p$-rank strata of the moduli spaces with parahoric level structure. Finer results are obtained on the Siegel 3-fold with Iwahori level structure.

任意抛物子群水平下基本非分歧 $GU(1,n-1)$ Rapoport-Zink 空间的 Bruhat-Tits 分层

The Bruhat-Tits stratification for basic unramified $GU(1,n-1)$ Rapoport-Zink spaces at arbitrary parahoric level

本文对签名 $(1,n-1)$ 的基本非分歧酉 Rapoport-Zink 空间在任意抛物子群水平下的约化特殊纤维进行分层，证明了闭分层的光滑性、不可约性并计算了维数，同时利用 Bruhat-Tits 指标描述了分层间的关联关系。

有理性型affine Deligne-Lusztig变种的连通分量

The connected components of affine Deligne--Lusztig varieties

本文通过p-adic Hodge理论方法，全面解决了affine Deligne-Lusztig变种和局部Shimura变种的连通分量问题，并推导了关于Shimura变种积分模型的新几何结果。