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moduli spaces of abelian varieties

Journal of the Institute of Mathematics of Jussieu (1)

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CONGRUENCE RELATIONS FOR SHIMURA VARIETIES ASSOCIATED TO SOME UNITARY GROUPS
Oliver Bültel, Torsten Wedhorn
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 5 / Issue 2 / April 2006

Published online by Cambridge University Press:

07 December 2005, pp. 229-261

Print publication:

April 2006
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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.