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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.02638 |
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| _version_ | 1866913872195092480 |
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| author | Li, Shang |
| author_facet | Li, Shang |
| contents | The classification of equivariant toroidal embeddings of a reductive group over an algebraically closed field is combinatorial and does not depend on the characteristic of the base field. This suggests that there should exist ``universal'' toroidal embeddings for a Chevalley group scheme over $\mathbb{Z}$ which specialize to classical toroidal embeddings via base change. In this paper, we establish the existence of ``universal'' equivariant toroidal embeddings for split reductive group schemes over $\mathbb{Z}$. We also discuss several geometric properties of these embeddings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toroidal embedding of Chevalley groups over $\mathbb{Z}$ Li, Shang Algebraic Geometry The classification of equivariant toroidal embeddings of a reductive group over an algebraically closed field is combinatorial and does not depend on the characteristic of the base field. This suggests that there should exist ``universal'' toroidal embeddings for a Chevalley group scheme over $\mathbb{Z}$ which specialize to classical toroidal embeddings via base change. In this paper, we establish the existence of ``universal'' equivariant toroidal embeddings for split reductive group schemes over $\mathbb{Z}$. We also discuss several geometric properties of these embeddings. |
| title | Toroidal embedding of Chevalley groups over $\mathbb{Z}$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2506.02638 |