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

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.