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CONGRUENCE RELATIONS FOR SHIMURA VARIETIES ASSOCIATED TO SOME UNITARY GROUPS

Published online by Cambridge University Press:  07 December 2005

Oliver Bültel  and
Torsten Wedhorn
Oliver Bültel
Affiliation:
Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 288, 69120 Heidelberg, Germany ([email protected])
Torsten Wedhorn
Affiliation:
Mathematisches Institut, Universität Bonn, Beringstraβe 4, 53115 Bonn, Germany ([email protected])
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Abstract

In this paper we study the reduction to characteristic $p$ of the Shimura variety associated to a unitary group which has signature $(n-1,1)$ at its real place. We describe the Newton polygon, the Ekedahl–Oort, and the final stratification. In addition we examine the moduli space of $p$-isogenies using a variant of the local model for Shimura varieties. We apply our results to obtain a proof of the Eichler–Shimura congruence relation for the case that $n$ is even.

Keywords

Shimura varietiescongruence relationsmoduli spaces of abelian varietiesPrimary 11G18Secondary 14G3514L0514K10
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 5 , Issue 2 , April 2006 , pp. 229 - 261
Copyright
2005 Cambridge University Press

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