Geodesic
On the fibration method for zero-cycles and rational points
Yonatan Harpaz1 ; Olivier Wittenberg2
1 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Nijmegen, The Netherlands
2 Département de mathématiques et applications, École normale supérieure, Paris, France
Annals of mathematics, Tome 183 (2016) no. 1, pp. 229-295.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2016.183.1.5

Yonatan Harpaz 1 ; Olivier Wittenberg 2

1 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Nijmegen, The Netherlands
2 Département de mathématiques et applications, École normale supérieure, Paris, France 
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Yonatan Harpaz; Olivier Wittenberg. On the fibration method for zero-cycles and rational points. Annals of mathematics, Tome 183 (2016) no. 1, pp. 229-295. doi : 10.4007/annals.2016.183.1.5. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.1.5/

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