2024/05/10 by Ioannis Zachos, Zhihao Zhao, Zachos, Ioannis +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2405.06163
openalex publication_date 2024/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Shimura varieties associated to a unitary group of signature (n-1, 1). For these varieties, we construct p-adic integral models over odd primes p which ramify in the imaginary quadratic field with level subgroup at p given by the stabilizer of a vertex lattice in the hermitian space. Our models are given by a variation of the construction of the splitting models of Pappas-Rapoport and they have a simple moduli theoretic description. By an explicit calculation, we show that these splitting models are normal, flat, Cohen-Macaulay and with reduced special fiber. In fact, they have relatively simple singularities: we show that a single blow-up along a smooth codimension one subvariety of the special fiber produces a semi-stable model. This also implies the existence of semi-stable models of the corresponding Shimura varieties.