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

2023/09/28 by Zachos, Ioannis, Zhao, Zhihao · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.16463

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 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.

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