Applications of the fibration method to the Brauer–Manin obstruction to the existence of zero-cycles on certain varieties

Abstract

We study the Brauer–Manin obstruction to the existence of zero-cycles of degree [Formula: see text] on certain classes of varieties over number fields. We generalize existing results in the literature and prove some results about fibrations over the projective line, where the geometric Brauer group of the generic fiber is not assumed to be finite. The idea is to assume that the Brauer–Manin obstruction to the Hasse principle is the only one for certain fibers and then deduce analogous results for zero-cycles.