On the fibration method for zero-cycles and rational points

• 成果类型: Article
• 署名作者: Harpaz, Yonatan; Wittenberg, Olivier
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.183.1.5
• 发表日期: 2016
• 页码: 229-295
• 关键词: brauer-manin obstruction; local-global principle; severi-brauer; weak approximation; hasse principle; chow groups; VARIETIES; descent; COHOMOLOGY; pencils

摘要

Conjectures on the existence of zero-cycles on arbitrary smooth projective varieties over number fields were proposed by Colliot-Thelene, Sansuc, Kato and Saito in the 1980's. We prove that these conjectures are compatible with fibrations, for fibrations into rationally connected varieties over a curve. In particular, they hold for the total space of families of homogeneous spaces of linear groups with connected geometric stabilisers. We prove the analogous result for rational points, conditionally on a conjecture on locally split values of polynomials which a recent work of Matthiesen establishes in the case of linear polynomials over the rationals.