Semi-stable and splitting models for unitary Shimura varieties over ramified places. II
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916827441922048 |
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| author | Zachos, Ioannis Zhao, Zhihao |
| author_facet | Zachos, Ioannis Zhao, Zhihao |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_06163 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semi-stable and splitting models for unitary Shimura varieties over ramified places. II Zachos, Ioannis Zhao, Zhihao Number Theory Algebraic Geometry 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. |
| title | Semi-stable and splitting models for unitary Shimura varieties over ramified places. II |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2405.06163 |