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

TL;DR

This paper constructs explicit smooth and regular integral models for certain unitary Shimura varieties over ramified primes, providing a detailed moduli interpretation and local model resolution.

Contribution

It introduces new explicit integral models for unitary Shimura varieties at ramified primes with detailed moduli descriptions and local model resolutions.

Findings

Constructed smooth p-adic integral models for s=1.

Developed regular p-adic integral models for s=2 and 3.

Provided explicit moduli-theoretic descriptions and local model resolutions.

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 $\pi$-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.