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Regular integral models for Shimura varieties of orthogonal type

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  15 June 2022

G. Pappas  and
I. Zachos
G. Pappas
Affiliation:
Department of Mathematics, Michigan State University, E. Lansing, MI 48824, USA pappasg@msu.edu
I. Zachos
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467, USA zachosi@bc.edu
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Abstract

We consider Shimura varieties for orthogonal or spin groups acting on hermitian symmetric domains of type IV. We give regular $p$-adic integral models for these varieties over odd primes $p$ at which the level subgroup is the connected stabilizer of a vertex lattice in the orthogonal space. Our construction is obtained by combining results of Kisin and the first author with an explicit presentation and resolution of a corresponding local model.

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties
Secondary: 14G35: Modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 158 , Issue 4 , April 2022 , pp. 831 - 867
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Copyright
© 2022 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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Footnotes

The first author acknowledges support by NSF grant DMS-2100743.

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