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On the flatness of models of certain Shimura varieties of PEL-type

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Abstract.

Consider a PEL-Shimura variety associated to a unitary group that splits over an unramified extension of \(\Q_p\). Rapoport and Zink have defined a model of the Shimura variety over the ring of integers of the completion of the reflex field at a place lying over p, with parahoric level structures at p. We show that this model is flat, as conjectured by Rapoport and Zink, and that its special fibre is reduced.

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  1. Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany (e-mail: ugoertz@mi.uni-koeln.de), , , , , , DE

    Ulrich Görtz

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  1. Ulrich Görtz
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Received: 11 September 2000 / Published online: 24 September 2001

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Görtz, U. On the flatness of models of certain Shimura varieties of PEL-type. Math Ann 321, 689–727 (2001). https://doi.org/10.1007/s002080100250

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  • DOI: https://doi.org/10.1007/s002080100250

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