Local models in the ramified case, II: Splitting models

Abstract

We study the reduction of certain PEL Shimura varieties with parahoric level structure at primes p at which the group that defines the Shimura variety ramifies. We describe ``good'' p-adic integral models of these Shimura varieties and study their etale local structure. In particular, we exhibit a stratification of their (singular) special fibers and give a partial calculation of the sheaf of nearby cycles.