Towards the Brauer–Manin obstruction on varieties fibred over the projective line

Abstract

Recently Dasheng Wei proved that the Brauer–Manin obstruction is the only obstruction to the Hasse principle for 0-cycles of degree 1 on some fibrations over the projective line defined by bi-cyclic normic equations. In the present paper, we prove the exactness of the global-to-local sequence for Chow groups of 0-cycles of such varieties. This signifies that the Brauer–Manin obstruction is also the only obstruction to weak approximation for 0-cycles of arbitrary degree. Our main theorem also generalizes several existing results.