On the fibration method for zero-cycles and rational points
On the fibration method for zero-cycles and rational points
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DOI：
10.4007/annals.2016.183.1.5
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发表时间：
2014-09
期刊：
影响因子：
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通讯作者：
Yonatan Harpaz;Olivier Wittenberg
中科院分区：
文献类型：
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作者：
Yonatan Harpaz;Olivier Wittenberg
关于数域上任意光滑射影簇上零圈存在性的猜想是由Colliot-Th\'el\' ene，Sanjiang，Kato和Saito在20世纪80年代提出的.我们证明，这些结构是兼容的纤维化，纤维化成理性连接品种的曲线。特别地，它们对于具有连通几何稳定子的线性群的齐性空间的族的全空间成立。我们证明了类似的结果合理的点，有条件的猜想上的局部分裂值的多项式，最近的工作Matthiesen建立的情况下，线性多项式的理性。
Conjectures on the existence of zero-cycles on arbitrary smooth projective varieties over number fields were proposed by Colliot-Th\'el\`ene, 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.