论文标题
霍奇类型的Shimura品种的积分模型中的归一化
Normalization in integral models of Shimura varieties of Hodge type
论文作者
论文摘要
令$（g，x）$为hodge类型的shimura基准，而$ \ mathscr {s} _k（g，x）$其积分模型具有hyperspecial（分别是帕拉赫，假设该组不受影响）级别结构。我们证明，$ \ mathscr {s} _k（g，x）$承认与模量解释兼容的封闭嵌入到整体模型$ \ mathscr {s} _ {k'} _} _} _}（\ \ m mathrm {gsp}，s^{\ pm pm}，s^{\ pm}），s^{\ pm}）$ for siegel modull a siegel modular vorth a siegel vorth。特别是，在$ \ mathscr {s} _k（g，x）$构建中的归一化步骤是多余的。特别是，我们的结果适用于Rapoport，Kottwitz等构建的早期积分模型（分别Rapoport-Zink等），因为这些模型与适当选择的Shimura数据的Hodge类型积分模型一致。 此外，结合LAN在整体模型的环形紧凑型边界组件上的结果，我们的结果还意味着，对于锥体分解的合适选择，hodge类型的整体模型的整体模型的环形模型的旋带压缩存在封闭式嵌入。
Let $(G,X)$ be a Shimura datum of Hodge type, and $\mathscr{S}_K(G,X)$ its integral model with hyperspecial (resp. parahoric, assuming the group is unramified) level structure. We prove that $\mathscr{S}_K(G,X)$ admits a closed embedding, which is compatible with moduli interpretations, into the integral model $\mathscr{S}_{K'}(\mathrm{GSp},S^{\pm})$ for a Siegel modular variety. In particular, the normalization step in the construction of $\mathscr{S}_K(G,X)$ is redundant. In particular, our results apply to the earlier integral models constructed by Rapoport, Kottwitz etc. (resp. Rapoport-Zink etc.), as those models agree with the Hodge type integral models for appropriately chosen Shimura data. Moreover, combined with a result of Lan's on the boundary components of toroidal compactifications of integral models, our result also implies that there exist closed embeddings of toroidal compactifications of integral models of Hodge type into toroidal compactifications of Siegel integral models, for suitable choices of cone decompositions.
