Congruence relations for Shimura varieties associated to some unitary groups

Details Congruence relations for Shimura varieties associated to some unitary groups Congruence relations for Shimura varieties associated to some unitary groups

2002-02-04

arxiv.org/abs/math/0202026v1

Mathematics

Algebraic Geometry

42 pages

Scientific paper

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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