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

Abstract 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 -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.