On the geometry of splitting models

2025/01/10 by Bijakowski, S., Zachos, I., Zhao, Z. · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2501.05950

Abstract

We consider Shimura varieties associated to a unitary group of signature (n-s,s) where n is even. For these varieties, by using the spin splitting models from Zachos-Zhao, we construct flat, Cohen-Macaulay, and normal p-adic integral models with reduced special fiber and with an explicit moduli-theoretic description 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. We prove that the special fiber of the corresponding splitting model is stratified by an explicit poset with a combinatorial description, similar to Bijakowski-Hernandez, and we describe its irreducible components. Additionally, we prove the closure relations for this stratification.

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