利用调节子重构算术基本群的分解子群
Reconstructing decomposition subgroups in arithmetic fundamental groups using regulators
摘要：
本文的主要目的是说明如何在算术曲线的基本群内重建点的分解子群和范数，如果给定以下数据：基本群，分圆特征标的一部分和给定曲线的所有代数覆盖的泛点所对应的域的调节子族.该方法受到Tamagawa关于有限域上曲线的方法的启发，但使用Tsfasman-Vlsoul定理代替Lefschetz迹公式。据作者所知，这是算术曲线的阿那贝尔几何中的一种新技术。它是有条件的，并且依赖于算术基本群的未知性质。我们还通过Iwasawa理论给出了一种新的方法来处理边界上的局部对应。
英文摘要：
Our main goal in the present article is to explain how one can reconstruct the decomposition subgroups and norms of points on an arithmetic curve inside its fundamental group if the following data are given: the fundamental group, a part of the cyclotomic character and the family of the regulators of the fields corresponding to the generic points of all étale covers of the given curve. The approach is inspired by that of Tamagawa for curves over finite fields but uses Tsfasman-Vlăduţ theorem instead of Lefschetz trace formula. To the authors' knowledge, this is a new technique in the anabelian geometry of arithmetic curves. It is conditional and depends on still unknown properties of arithmetic fundamental groups. We also give a new approach via Iwasawa theory to the local correspondence at the boundary.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
