Wildly ramified unitary local models for special parahorics. The odd dimensional case
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909736116420608 |
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| author | Yang, Jie |
| author_facet | Yang, Jie |
| contents | We construct local models for wildly ramified unitary similitude groups of odd dimension $n\geq 3$ with special parahoric level structure and signature $(n-1,1)$. We first give a lattice-theoretic description for parahoric subgroups using Bruhat-Tits theory in residue characteristic two, and apply them to define local models following the lead of Rapoport-Zink and Pappas-Rapoport. In our case, there are two conjugacy classes of special parahoric subgroups. We show that the local models are smooth for the one class and normal, Cohen-Macaulay for the other class. We also prove that they represent the v-sheaf local models of Scholze-Weinstein. Under some additional assumptions, we obtain an explicit moduli interpretation of the local models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wildly ramified unitary local models for special parahorics. The odd dimensional case Yang, Jie Number Theory Algebraic Geometry We construct local models for wildly ramified unitary similitude groups of odd dimension $n\geq 3$ with special parahoric level structure and signature $(n-1,1)$. We first give a lattice-theoretic description for parahoric subgroups using Bruhat-Tits theory in residue characteristic two, and apply them to define local models following the lead of Rapoport-Zink and Pappas-Rapoport. In our case, there are two conjugacy classes of special parahoric subgroups. We show that the local models are smooth for the one class and normal, Cohen-Macaulay for the other class. We also prove that they represent the v-sheaf local models of Scholze-Weinstein. Under some additional assumptions, we obtain an explicit moduli interpretation of the local models. |
| title | Wildly ramified unitary local models for special parahorics. The odd dimensional case |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2406.16774 |