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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2511.00824 |
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| _version_ | 1866911297532067840 |
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| author | Cao, Yang Wang, Yijin |
| author_facet | Cao, Yang Wang, Yijin |
| contents | Let $G$ be a connected linear algebraic group over a number field $K$. In this article, we study the almost strong approximation property (ASA) of $G$ raised by Rapinchuk and Tralle. Building on Demarche's results on strong approximation with Brauer-Manin obstruction, we introduce a necessary and sufficient condition for (ASA) to hold in terms of the Brauer group of $G$. Using the criteria, we conclude that (ASA) can be completely controlled by the Dirichlet density of the places and the splitting field of $G$, which generalizes a result of Rapinchuk and Tralle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On almost strong approximation for linear algebraic groups Cao, Yang Wang, Yijin Number Theory Algebraic Geometry 14G12 Let $G$ be a connected linear algebraic group over a number field $K$. In this article, we study the almost strong approximation property (ASA) of $G$ raised by Rapinchuk and Tralle. Building on Demarche's results on strong approximation with Brauer-Manin obstruction, we introduce a necessary and sufficient condition for (ASA) to hold in terms of the Brauer group of $G$. Using the criteria, we conclude that (ASA) can be completely controlled by the Dirichlet density of the places and the splitting field of $G$, which generalizes a result of Rapinchuk and Tralle. |
| title | On almost strong approximation for linear algebraic groups |
| topic | Number Theory Algebraic Geometry 14G12 |
| url | https://arxiv.org/abs/2511.00824 |