Arithmetic of Châtelet surface bundles revisited

Abstract

We study arithmetic of the algebraic varieties defined over number fields by applying Lagrange interpolation to fibrations. Assuming the finiteness of the Tate-Shafarevich group of a certain elliptic curve, we show, for Châtelet surface bundles over curves, that the violation of Hasse principle being accounted for by the Brauer-Manin obstruction is not invariant under an arbitrary finite extension of the ground field.

Comments are welcome

References in corpus (3)

• Quadratic points on intersections of two quadrics
• Châtelet surfaces and non-invariance of the Brauer-Manin obstruction for $3$-folds
• Non-invariance of the Brauer-Manin obstruction for surfaces