由Q̄*中有限秩子群生成的域
数论
2021-05-11 v2
摘要
设Γ为Q̄*的一个有限秩子群。我们证明由Γ的可除包中所有元素生成的域的乘法群，模该可除包是自由阿贝尔的。这证明了Rémond广义Lehmer猜想的一个必要条件得到满足。
引用
@article{arxiv.1910.11636,
title = {Fields Generated by Finite Rank Subgroups of $\overline{\mathbb{Q}}^*$},
author = {Lukas Pottmeyer},
journal= {arXiv preprint arXiv:1910.11636},
year = {2021}
}
备注
A serious error was found in the proof of the former Lemma 5.1 which could not be fixed. Since the result concerning elliptic curves in the former Theorem 1.2 was dependent on this lemma, this result and Sections 5, 6, and 7, were removed. The new version now only contains the proof of the result on the linear torus