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Local models in the ramified case. III Unitary groups

Part of: Arithmetic problems. Diophantine geometry Special varieties Arithmetic algebraic geometry

Published online by Cambridge University Press:  26 March 2009

G. Pappas  and
M. Rapoport
G. Pappas
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA, (pappas@math.msu.edu).
M. Rapoport
Affiliation:
Mathematisches Institut der Universität Bonn, Beringstrasse 1, 53115 Bonn, Germany, (rapoport@math.uni-bonn.de).
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Abstract

We continue our study of the reduction of PEL Shimura varieties with parahoric level structure at primes p at which the group defining the Shimura variety ramifies. We describe ‘good’ p-adic integral models of these Shimura varieties and study their étale local structure. In the present paper we mainly concentrate on the case of unitary groups for a ramified quadratic extension. Some of our results are applications of the theory of twisted affine flag varieties that we developed in a previous paper.

Keywords

Shimura varietyunitary groupparahoric subgrouplocal model

MSC classification

Secondary: 14G35: Modular and Shimura varieties 11G18: Arithmetic aspects of modular and Shimura varieties 14M15: Grassmannians, Schubert varieties, flag manifolds
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 8 , Issue 3 , July 2009 , pp. 507 - 564
Copyright
Copyright © Cambridge University Press 2009

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