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On Goren–Oort stratification for quaternionic Shimura varieties
- Part of
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- Journal:
- Compositio Mathematica / Volume 152 / Issue 10 / October 2016
- Published online by Cambridge University Press:
- 21 September 2016, pp. 2134-2220
- Print publication:
- October 2016
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- Article
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- You have access
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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 
$p$ .
