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We study some integral model of P.E.L. Shimura varieties of type A forramified primes. Precisely, we look at the Pappas-Rapoport model (or splittingmodel) of some unitary Shimura varieties for which there is ramification in thedegree 2 CM extension. We show that the model isn't smooth, but that it isnormal with Cohen-Macaulay special fiber. We moreover study its special fiberby introducing a combinatorial stratification for which we can compute theclosure relations. Even if there are "extra" components in special fiber, weprove that those do not contribute to mod p modular forms in regular degree. Wealso study the interaction of the stratification with the naturalstratification given by the vanishing of some partial Hasse invariants, in thecase of signature (1,n-1).

On the geometry of the Pappas-Rapoport models in the (AR) case