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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.05017 |
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| _version_ | 1866912497451139072 |
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| author | Hu, Yong Tian, Yisheng |
| author_facet | Hu, Yong Tian, Yisheng |
| contents | We prove some triviality results for reduced Whitehead groups and reduced unitary Whitehead groups for division algebras over a henselian discrete valuation field whose residue field has virtual cohomological dimension or separable dimension $\le 2$. These results are applied to show strong approximation for isotropic absolutely almost simple simply connected groups of type A. In particular, such a group defined over the function field of a nonreal curve $C/k$ satisfies strong approximation if the base field $k$ is a number field, a $p$-adic field, $\mathbb{C}(\!(t)\!)$ or a two-variable function field over $\mathbb{R}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Trivialité des groupes de Whitehead réduits avec applications à l'approximation faible et l'approximation forte Hu, Yong Tian, Yisheng Number Theory Algebraic Geometry 11E57 19B99 20G35 16K20 We prove some triviality results for reduced Whitehead groups and reduced unitary Whitehead groups for division algebras over a henselian discrete valuation field whose residue field has virtual cohomological dimension or separable dimension $\le 2$. These results are applied to show strong approximation for isotropic absolutely almost simple simply connected groups of type A. In particular, such a group defined over the function field of a nonreal curve $C/k$ satisfies strong approximation if the base field $k$ is a number field, a $p$-adic field, $\mathbb{C}(\!(t)\!)$ or a two-variable function field over $\mathbb{R}$. |
| title | Trivialité des groupes de Whitehead réduits avec applications à l'approximation faible et l'approximation forte |
| topic | Number Theory Algebraic Geometry 11E57 19B99 20G35 16K20 |
| url | https://arxiv.org/abs/2401.05017 |