Principe local-global pour les z\'ero-cycles sur certaines fibrations au-dessus de l'espace projectif

Abstract

We study the local-global principle for zero-cycles of degree 1 on certain varieties fibered over the projective space. Among other applications, we prove that the Brauer-Manin obstruction is the only obstruction to the Hasse principle and weak approximation for zero-cycles of degree 1 on Severi-Brauer-variety bundles or Ch\^atelet-surface bundles over the projective space.