论文标题
mod $ p $点的帕哈里卡级别的shimura品种（带有Rong Zhou的附录）
Mod $p$ points on Shimura varieties of parahoric level (with an appendix by Rong Zhou)
论文作者
论文摘要
我们研究了霍奇类型的Shimura品种的Kisin-Pappas积分模型的mod $ p $ - 点。我们表明，如果该组是准切片，则每个同学类别都包含一个CM点的降低，证明了Kisin-madapusi-pera-shin的猜想。我们此外表明，mod $ p $同一类是兰格兰兹预测的形式 - 罗波特猜想，如果shimura品种合适，或者如果$ p $的群体不受影响。我们工作中的主要成分是一个全球论点，它使我们能够将猜想减少到非常特殊的帕哈里奇级别的情况下。 Rong Zhou在附录中处理此情况。作为我们论点的推论，我们确定了Ekedahl - Oort阶层的连接组成部分。
We study the mod $p$-points of the Kisin--Pappas integral models of Shimura varieties of Hodge type with parahoric level. We show that if the group is quasi-split, then every isogeny class contains the reduction of a CM point, proving a conjecture of Kisin--Madapusi-Pera--Shin. We furthermore show that the mod $p$ isogeny classes are of the form predicted by the Langlands--Rapoport conjecture if either the Shimura variety is proper or if the group at $p$ is unramified. The main ingredient in our work is a global argument that allows us to reduce the conjecture to the case of very special parahoric level. This case is dealt with in the appendix by Rong Zhou. As a corollary to our arguments, we determine the connected components of Ekedahl--Oort strata.
