On the fibration method for zero-cycles and rational points
arXiv:1409.0993 · doi:10.4007/annals.2016.183.1.5
Abstract
Conjectures on the existence of zero-cycles on arbitrary smooth projective varieties over number fields were proposed by Colliot-Thélène, 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.
54 pages; v3: minor updates, added Remark 9.12(ii), v4: improved exposition, final version
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Cited by in corpus (19)
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