Arithmetic of Ch\^atelet surface bundles revisited

We study arithmetic of the algebraic varieties defined over number fields by applying Lagrange interpolation to fibrations. Assuming a conjecture of M. Stoll, 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.