Semi-stable and Splitting Models for Unitary Shimura Varieties Over Ramified Places. II.

Abstract We consider Shimura varieties associated to a unitary group of signature $(n-1,1)$. For these varieties, we construct $p$-adic integral models over odd primes $p$ which ramify in the imaginary quadratic field with level subgroup at $p$ given by the stabilizer of a vertex lattice in the hermitian space. Our models are given by a variation of the construction of the splitting models of Pappas–Rapoport and they have a simple moduli theoretic description. By an explicit calculation, we show that these splitting models are normal, flat, Cohen–Macaulay and with reduced special fiber. In fact, they have relatively simple singularities: we show that a single blow-up along a smooth codimension one subvariety of the special fiber produces a semi-stable model. This also implies the existence of semi-stable models of the corresponding Shimura varieties.