LULU is syntomic
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914784122765312 |
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| author | Lima-Filho, Paulo Elizondo, E. Javier |
| author_facet | Lima-Filho, Paulo Elizondo, E. Javier |
| contents | Let $G$ be a Chevalley group over a field $\Bbbk$. Fix a maximal torus $\mathbb{T}$ in $ G $, along with opposite Borel subgroups $ B $ and $ B^-$ satisfying $ \mathbb{T} = B \cap B^-$, and denote by $ \mathbb{U} := R_u(B) $ and $ \mathbb{L} := R_u(B^-)$ their respective unipotent radicals. We prove that the multiplication map $ μ\colon \mathbb{L} \times \mathbb{U}\times \mathbb{L} \times \mathbb{U} \longrightarrow G $ is syntomic and faithfully flat over any base field $ \Bbbk$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02701 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | LULU is syntomic Lima-Filho, Paulo Elizondo, E. Javier Algebraic Geometry 20G15, 14N20, 13F55 Let $G$ be a Chevalley group over a field $\Bbbk$. Fix a maximal torus $\mathbb{T}$ in $ G $, along with opposite Borel subgroups $ B $ and $ B^-$ satisfying $ \mathbb{T} = B \cap B^-$, and denote by $ \mathbb{U} := R_u(B) $ and $ \mathbb{L} := R_u(B^-)$ their respective unipotent radicals. We prove that the multiplication map $ μ\colon \mathbb{L} \times \mathbb{U}\times \mathbb{L} \times \mathbb{U} \longrightarrow G $ is syntomic and faithfully flat over any base field $ \Bbbk$. |
| title | LULU is syntomic |
| topic | Algebraic Geometry 20G15, 14N20, 13F55 |
| url | https://arxiv.org/abs/2405.02701 |