Semi-stable and splitting models for unitary Shimura varieties over ramified places. I
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911060774092800 |
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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 $(n-s,s)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16463 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semi-stable and splitting models for unitary Shimura varieties over ramified places. I Zachos, Ioannis Zhao, Zhihao Number Theory Algebraic Geometry 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. |
| title | Semi-stable and splitting models for unitary Shimura varieties over ramified places. I |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2309.16463 |