Brauer groups of conic bundles over elliptic curves

2025/09/19 by Alfaraj, Abdulmuhsin
#14F22 #14G12 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.16051

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 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.

Citations

• The elliptic sieve and Brauer groups

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