2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63963This paper is a continuation of our paper math.AG/0006222. 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.LaTeX, 51 pages, to appear in the Duke Math. JournalAlgebraic Geometry14G35; 11G18text