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Rapoport–Zink spaces for spinor groups

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  10 April 2017

Benjamin Howard  and
Georgios Pappas
Benjamin Howard
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467-3806, USA email howardbe@bc.edu
Georgios Pappas
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA email pappas@math.msu.edu
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Abstract

After the work of Kisin, there is a good theory of canonical integral models of Shimura varieties of Hodge type at primes of good reduction. The first part of this paper develops a theory of Hodge type Rapoport–Zink formal schemes, which uniformize certain formal completions of such integral models. In the second part, the general theory is applied to the special case of Shimura varieties associated with groups of spinor similitudes, and the reduced scheme underlying the Rapoport–Zink space is determined explicitly.

Keywords

Shimura varietyspinor groupRapoport–Zink space

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties 14G35: Modular and Shimura varieties
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 5 , May 2017 , pp. 1050 - 1118
Copyright
© The Authors 2017 

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