Brauer groups of conic bundles over elliptic curves
Abstract
Abstract 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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Geometric and Algebraic Topology
Publication details
- Journal / source
- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 15 April 2026
- Language
- EN