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arXiv · 2405.06163

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

Ioannis Zachos·Zhihao Zhao
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Abstract

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.

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Ioannis Zachos, Zhihao Zhao. 2024-05-10. Semi-stable and splitting models for unitary Shimura varieties over ramified places. II. https://arxiv.org/abs/2405.06163

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