函数域上广义Hurwitz空间与二次扭族Selmer群的同调稳定性
数论
2025-01-28 v3 代数几何
代数拓扑
摘要
我们证明了全局函数域上阿贝尔簇二次扭族Selmer群的Bhargava-Kane-Lenstra-Poonen-Rains启发式的一个版本。作为推论，我们导出了关于此类族中阿贝尔簇Selmer秩的“极简主义猜想”的一个结果。更确切地说，我们表明这两个猜想中预测的概率在常数域的大小意义上的误差项内是正确的，且当增长时该误差趋于。两个关键输入是：参数化任意亏格穿孔黎曼曲面覆盖的广义Hurwitz空间版本的一个新同调稳定性定理，以及Selmer群平均大小用这些Hurwitz空间在有限域上有理点数表示的表达式。
引用
@article{arxiv.2310.16286,
title = {Homological stability for generalized Hurwitz spaces and Selmer groups in quadratic twist families over function fields},
author = {Jordan S. Ellenberg and Aaron Landesman},
journal= {arXiv preprint arXiv:2310.16286},
year = {2025}
}
备注
We incorrectly thought the Fulton Macpherson compactification of configuration spaces on open curves was compact. Due to this mistake, we had to construct a suitable compactification ourselves, which resulted in Appendix B, jointly written by Dori Bejleri and Aaron Landesman