分裂型toric栈有理点多高度分布
数论
2026-03-16 v2 代数几何
摘要
我们研究分裂型toric栈有理点的分布，其所有高度均受Q限制，通过将计数问题提升到与toric栈关联的orbifold Picard群下面的扩展普遍torus下来实现。为此，我们证明了toric栈上有理点存在积分参数化，这使我们能够定义将栈式高度提升到该扩展普遍torus下的函数。这允许我们将toric栈的Tamagawa数定义为欧拉积，并对于素数p，通过计数toric栈各sector的F_p点来解释p-原子因子。
引用
@article{arxiv.2510.22325,
title = {Multi-height distribution of rational points of split toric stacks},
author = {Nicolas Bongiorno},
journal= {arXiv preprint arXiv:2510.22325},
year = {2026}
}
备注
The previous version contained errors in the computation of the type of the torsor arising from the usual quotient presentation of toric stacks and in the computation of the leading constant. These have now been corrected. The previous version only treated the torsion-free Picard group case, while the present version treats the general case