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Congruence relations for Shimura varieties associated to some unitary groups

O. Bueltel·T. Wedhorn
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Abstract

In this paper we study the reduction of PEL-Shimura varieties associated to unitary groups of signature (n-1,1) in the inert and unramified case. We describe the Newton polygon and the Ekedahl-Oort stratification. We further study the associated moduli space of isogenies and use a variant of the local model to give a generic description. As an application we prove a conjecture of Blasius und Rogawski about the congruence relation if the integer n is even.

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O. Bueltel, T. Wedhorn. 2002-02-04. Congruence relations for Shimura varieties associated to some unitary groups. https://arxiv.org/abs/math/0202026

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