Semi-stable and splitting models for unitary Shimura varieties over ramified places. I.

We consider Shimura varieties associated to a unitary group of signature $(n-s,s)$ where n is even. For these varieties, we construct smooth p -adic integral models for $s=1$ and regular p -adic integral models for $s=2$ and $s=3$ over odd primes p which ramify in the imaginary quadratic field with level subgroup at p given by the stabilizer of a π -modular lattice in the hermitian space. Our construction, which has an explicit moduli-theoretic description, is given by an explicit resolution of a corresponding local model.