On the flatness of spin local models for split even orthogonal groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918501390745600 |
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| author | Yang, Jie |
| author_facet | Yang, Jie |
| contents | Let $F$ be a complete discretely valued field with ring of integers $\mathcal{O}$ and residue field of characteristic $p>2$. Let $G=\operatorname{GO}_{2n}$ denote the split orthogonal similitude group over $F$. For any parahoric level structure, we prove that the associated spin local model for $G$ is a flat $\mathcal{O}$-scheme with reduced special fiber. This confirms a conjecture of Pappas and Rapoport in the split case. As a corollary, we construct a flat (integral) moduli space of PEL-type D. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the flatness of spin local models for split even orthogonal groups Yang, Jie Number Theory Let $F$ be a complete discretely valued field with ring of integers $\mathcal{O}$ and residue field of characteristic $p>2$. Let $G=\operatorname{GO}_{2n}$ denote the split orthogonal similitude group over $F$. For any parahoric level structure, we prove that the associated spin local model for $G$ is a flat $\mathcal{O}$-scheme with reduced special fiber. This confirms a conjecture of Pappas and Rapoport in the split case. As a corollary, we construct a flat (integral) moduli space of PEL-type D. |
| title | On the flatness of spin local models for split even orthogonal groups |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.16704 |