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

TL;DR

This paper constructs regular p-adic integral models for certain unitary Shimura varieties over ramified primes, using explicit resolutions of local models to handle singularities.

Contribution

It provides the first explicit regular integral models for these Shimura varieties at ramified primes, advancing understanding of their arithmetic geometry.

Findings

Successfully constructed regular p-adic models over ramified primes

Resolved singularities via explicit local model resolutions

Enhanced understanding of integral models for unitary Shimura varieties

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.