Local-global principle for 0-cycles on fibrations over rationally connected bases

Abstract

We study the Brauer-Manin obstruction to the Hasse principle and to weak approximation for 0-cycles on algebraic varieties that possess a fibration structure. The exactness of the local-to-global sequence $(E)$ of Chow groups of 0-cycles was known only for a fibration whose base is either a curve or the projective space. In the present paper, we prove the exactness of $(E)$ for fibrations whose bases are Châtelet surfaces or projective models of homogeneous spaces of connected linear algebraic groups with connected stabilizers. We require that either all fibres are split and most fibres satisfy weak approximation for 0-cycles, or the generic fibre has a 0-cycle of degree $1$ and $(E)$ is exact for most fibres.

20 pages. The introduction has been rewritten. More details of the applications of the main results are given. The proof of Th. 2.4 is removed, instead, a sketch is given at the end of the paper

References in corpus (1)

• The local-global exact sequence for Chow groups of zero-cycles