Mathematische Annalen

, Volume 321, Issue 3, pp 689–727 | Cite as

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

  • Ulrich Görtz


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.

Mathematics Subject Classification (1991): 14G35, 11G18 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ulrich Görtz
    • 1
  1. 1.Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 Köln, Germany (e-mail:

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