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On Goren–Oort stratification for quaternionic Shimura varieties

  • Yichao Tian (a1) and Liang Xiao (a2)

Abstract

Let $F$ be a totally real field in which a prime $p$ is unramified. We define the Goren–Oort stratification of the characteristic- $p$ fiber of a quaternionic Shimura variety of maximal level at $p$ . We show that each stratum is a $(\mathbb{P}^{1})^{r}$ -bundle over other quaternionic Shimura varieties (for an appropriate integer $r$ ). As an application, we give a necessary condition for the ampleness of a modular line bundle on a quaternionic Shimura variety in characteristic $p$ .

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On Goren–Oort stratification for quaternionic Shimura varieties

  • Yichao Tian (a1) and Liang Xiao (a2)

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