Regular models of ramified unitary Shimura varieties at maximal parahoric level

We use the idea of splitting models to define and study a semi-stable model for unitary Shimura varieties of signature $(n-1,1)$ with maximal parahoric level structure at ramified primes. In this case, the ``naive'' splitting model defined by Pappas and Rapoport fails to be flat in a crucial way. We prove that the genuine splitting model in this case is flat with semi-stable reduction.