数域循环p扩张的构造：其单位群的Galois模结构被规定
数论
2025-07-18 v1
摘要
对于任意有限循环p群G，我们将证明：每个Z_p- torsion-free的 finitely generated Z_p[G]-模，都可作为K的单位群K^×⊗_Z Z_p（在适当的G扩张K/k中）出现，最多只能出现Z_p[G]-free direct summand。
引用
@article{arxiv.2507.12949,
title = {Construction of a cyclic $p$-extension of number fields whose unit group has prescribed Galois module structure},
author = {Manabu Ozaki},
journal= {arXiv preprint arXiv:2507.12949},
year = {2025}
}