Semi-stable models for some unitary Shimura varieties over ramified primes

Abstract

We consider Shimura varieties associated to a unitary group of signature $(2,n-2)$. We give regular $p$-adic integral models for these varieties over odd primes $p$ which ramify in the imaginary quadratic field with level subgroup at $p$ given by the stabilizer of a selfdual lattice in the hermitian space. Our construction is given by an explicit resolution of a corresponding local model.