We study p-adic integral models of certain PEL-Shimura varieties with level subgroup at p given by the pro-unipotent radical of an Iwahori. We will consider two cases: the case of Shimura varieties associated with unitary groups that split over an unramified extension of Q_p and the case of Siegel modular varieties. We construct local models, i.e. simpler schemes which are etale locally isomorphic to the integral models. Our integral models are defined by a moduli scheme using the notion of an Oort-Tate generator of a group scheme. We use these local models to find a resolution of the integral model in the case of the Siegel modular variety of genus 2. The resolution is regular with special fiber a nonreduced divisor with normal crossings.
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