Approximation theorems for classifying stacks over number fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911063781408768 |
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| author | Dhillon, Ajneet |
| author_facet | Dhillon, Ajneet |
| contents | Approximation theorems for algebraic stacks over a number field $k$ are studied in this article. For G a connected linear algebraic group over a number field we prove strong approximation with Brauer-Manin obstruction for the classifying stack $BG$. This result answers a very concrete question, given $G$-torsors $P_v$ over $k_v$, where $v$ ranges over a finite number of places, when can you approximate the $P_v$ by a $G$-torsor $P$ defined over $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation theorems for classifying stacks over number fields Dhillon, Ajneet Number Theory 11G35, 14L99 Approximation theorems for algebraic stacks over a number field $k$ are studied in this article. For G a connected linear algebraic group over a number field we prove strong approximation with Brauer-Manin obstruction for the classifying stack $BG$. This result answers a very concrete question, given $G$-torsors $P_v$ over $k_v$, where $v$ ranges over a finite number of places, when can you approximate the $P_v$ by a $G$-torsor $P$ defined over $k$. |
| title | Approximation theorems for classifying stacks over number fields |
| topic | Number Theory 11G35, 14L99 |
| url | https://arxiv.org/abs/2507.13900 |