On the moduli description of ramified unitary local models of signature $(n-1,1)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913833081110528 |
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| author | Luo, Yu |
| author_facet | Luo, Yu |
| contents | We provide a moduli description of the ramified unitary local model of signature $(n-1,1)$ with arbitrary parahoric level structure, assuming the residue field has characteristic not equal to $2$, thereby confirming a conjecture of Smithling. Our approach involves writing down explicit equations for the special fiber and proving that they define a normal, Cohen-Macaulay scheme, which is also of independent interest. As applications, we obtain moduli descriptions for: (1) ramified unitary Pappas-Zhu local models with arbitrary parahoric level; (2) the irreducible components of their special fiber in the maximal parahoric case; (3) integral models of ramified unitary Shimura varieties with arbitrary (quasi-)parahoric level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10723 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the moduli description of ramified unitary local models of signature $(n-1,1)$ Luo, Yu Algebraic Geometry Number Theory We provide a moduli description of the ramified unitary local model of signature $(n-1,1)$ with arbitrary parahoric level structure, assuming the residue field has characteristic not equal to $2$, thereby confirming a conjecture of Smithling. Our approach involves writing down explicit equations for the special fiber and proving that they define a normal, Cohen-Macaulay scheme, which is also of independent interest. As applications, we obtain moduli descriptions for: (1) ramified unitary Pappas-Zhu local models with arbitrary parahoric level; (2) the irreducible components of their special fiber in the maximal parahoric case; (3) integral models of ramified unitary Shimura varieties with arbitrary (quasi-)parahoric level. |
| title | On the moduli description of ramified unitary local models of signature $(n-1,1)$ |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2404.10723 |