Journal of the Institute of Mathematics of Jussieu · 2005 · 41 citations · 2 references
Natural SciencesMathematicsComputational GeometryGeometryNumber TheoryAbstract AlgebraAlgebraic GeometryArithmetic GeometryGalois TheoryGroup TheoryShimura VarietiesStratification
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.
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