Kummer簇与K3曲面乘积上有理点及零圈的算术
数论
2023-03-10 v4 代数几何
摘要
设k为一个数域。秉承Yongqi Liang的一个结果之精神，我们将k的有限扩张上有理点的算术与k上零圈的算术对k上的Kummer簇联系起来。例如，对k上任意Kummer簇X，我们证明若Brauer-Manin阻碍是X在所有k的有限扩张上有理点的Hasse原理的唯一阻碍，则（2- primary）Brauer-Manin阻碍是X上k给定任意奇次零圈的Hasse原理的唯一阻碍。我们也得到了关于Kummer簇乘积、K3曲面及有理连通簇的类似结果。
引用
@article{arxiv.1805.12538,
title = {Arithmetic of rational points and zero-cycles on products of Kummer varieties and K3 surfaces},
author = {Francesca Balestrieri and Rachel Newton},
journal= {arXiv preprint arXiv:1805.12538},
year = {2023}
}
备注
16 pages. Corrected grant reference number and added journal reference and DOI. arXiv admin note: substantial text overlap with arXiv:1804.05819