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Article Dans Une Revue Annals of Mathematics Année : 2016

On the fibration method for zero-cycles and rational points

Résumé

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.

Dates et versions

hal-02371541 , version 1 (19-11-2019)

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Yonatan Harpaz, Olivier Wittenberg. On the fibration method for zero-cycles and rational points. Annals of Mathematics, 2016, 183 (1), pp.229-295. ⟨10.4007/annals.2016.183.1.5⟩. ⟨hal-02371541⟩
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