Principe local-global pour les zéro-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 Châtelet-surface bundles over the projective space.

arXiv commentIn French, 27 pages. Comparing to the version 3, Lemma 4.1 was not correct and hence has been removed in this version, the hypothesis (abelienne-scindee) has been slightly changed and the corresponding proofs have been fixed

Cited by in corpus (1)

• Towards the Brauer-Manin obstruction on varieties fibred over the projective line