论文标题
关于阳性特征的Shimura品种的叶子
Foliations on Shimura varieties in positive characteristic
论文作者
论文摘要
本文是[G-DS1]的延续。我们研究了Shimura品种的两种类型的叶子，特征$ p $。我们称为“重言式叶子”的第一个是在希尔伯特模块化品种上定义的，并提高到特征$ 0 $。第二个是“ $ v $ foliations”，仅在特征性$ p $的统一shimura品种上定义，并概括我们之前研究的叶子，当时所讨论的CM字段是二次假想的。我们确定这些叶子何时被$ p $ cluct，以及它们光滑的位置。在不光滑的情况下，我们构建了shimura品种的“连续炸毁”，它们作为光滑的叶子扩展到了。我们讨论叶子的一些整体品种。我们将Foliation的$ S $的商与来自同一类型的另一个Shimura品种的某个组成部分的纯粹不可分割的地图联系起来，而Parahoric级别的结构为$ P $，到$S。
This paper is a continuation of [G-dS1]. We study foliations of two types on Shimura varieties $S$ in characteristic $p$. The first, which we call "tautological foliations", are defined on Hilbert modular varieties, and lift to characteristic $0$. The second, the "$V$-foliations", are defined on unitary Shimura varieties in characteristic $p$ only, and generalize the foliations studied by us before, when the CM field in question was quadratic imaginary. We determine when these foliations are $p$-closed, and the locus where they are smooth. Where not smooth, we construct a "successive blow up" of our Shimura variety to which they extend as smooth foliations. We discuss some integral varieties of the foliations. We relate the quotient of $S$ by the foliation to a purely inseparable map from a certain component of another Shimura variety of the same type, with parahoric level structure at $p$, to $S.$
