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On Goren–Oort stratification for quaternionic Shimura varieties

Published online by Cambridge University Press:  21 September 2016

Yichao Tian
Affiliation:
Morningside Center of Mathematics, Chinese Academy of Sciences, 55 Zhong Guan Cun East Road, Beijing 100190, China email yichaot@math.ac.cn
Liang Xiao
Affiliation:
UConn Department of Mathematics, 196 Auditorium Road, Unit 3009, Storrs, CT 06269-3009, USA email liang.xiao@uconn.edu
Corresponding

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 $p$ .

Type
Research Article
Copyright
© The Authors 2016 

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