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ON THE GEOMETRY OF THE PAPPAS–RAPOPORT MODELS FOR PEL SHIMURA VARIETIES

Part of: Arithmetic problems. Diophantine geometry Algebraic groups Arithmetic algebraic geometry

Published online by Cambridge University Press:  18 February 2022

Stéphane Bijakowski  and
Valentin Hernandez Open the ORCID record for Valentin Hernandez [Opens in a new window]
Stéphane Bijakowski
Affiliation:
Centre de mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau, France ([email protected])
Valentin Hernandez*
Affiliation:
Laboratoire Mathématiques d’Orsay, Bâtiment 307, Université Paris-Sud, 91405 Orsay, France
*
[email protected]
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Abstract

In this article we study integral models of Shimura varieties, called Pappas–Rapoport splitting model, for ramified P.E.L. Shimira data. We study the special fiber and some stratification of these models, in particular we show that these are smooth and the Rapoport locus and the $\mu $-ordinary locus are dense, under some condition on the ramification.

Keywords

Shimura varietiesintegral models of Shimura varietiesp-divisible groupsNewton stratification

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties
Secondary: 14G35: Modular and Shimura varieties 14L05: Formal groups, $p$-divisible groups
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 5 , September 2023 , pp. 2403 - 2445
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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