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<p>We study the Brauer groups of regular conic bundles over elliptic curves defined over a number field <i>k</i>. We explicitly compute the Brauer group of the conic bundle when the singular fibres lie above <i>k</i>-points that are 2-torsion on the elliptic curve, and the corresponding splitting 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.</p>

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Brauer groups of conic bundles over elliptic curves

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  • 发表日期：

    2026年4月15日

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  • Abdulmuhsin Alfaraj

摘要

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 2-torsion on the elliptic curve, and the corresponding splitting 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.