On the geometry of splitting models
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916561294458880 |
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| author | Bijakowski, S. Zachos, I. Zhao, Z. |
| author_facet | Bijakowski, S. Zachos, I. Zhao, Z. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05950 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the geometry of splitting models Bijakowski, S. Zachos, I. Zhao, Z. 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, 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. |
| title | On the geometry of splitting models |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2501.05950 |