Brauer groups of conic bundles over elliptic curves
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916958043111424 |
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| author | Alfaraj, Abdulmuhsin |
| author_facet | Alfaraj, Abdulmuhsin |
| contents | We study the Brauer groups of regular conic bundles over elliptic curves defined over a number field $k$. We explicitly compute the Brauer group of the conic bundle when the singular fibres lie above $k$-points that are divisible by $2$ in $E(k)$, and the corresponding ramification fields are isomorphic. We apply the result to compute the Brauer group of a class of surfaces analogous to that of Châtelet surfaces. We investigate Brauer-Manin obstructions to weak approximation coming from the real places on such surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brauer groups of conic bundles over elliptic curves Alfaraj, Abdulmuhsin Algebraic Geometry Number Theory 14F22, 14G12 We study the Brauer groups of regular conic bundles over elliptic curves defined over a number field $k$. We explicitly compute the Brauer group of the conic bundle when the singular fibres lie above $k$-points that are divisible by $2$ in $E(k)$, and the corresponding ramification fields are isomorphic. We apply the result to compute the Brauer group of a class of surfaces analogous to that of Châtelet surfaces. We investigate Brauer-Manin obstructions to weak approximation coming from the real places on such surfaces. |
| title | Brauer groups of conic bundles over elliptic curves |
| topic | Algebraic Geometry Number Theory 14F22, 14G12 |
| url | https://arxiv.org/abs/2509.16051 |