Construction of a cyclic $p$-extension of number fields whose unit group has prescribed Galois module structure

Manabu Ozaki

Construction of a cyclic $p$-extension of number fields whose unit group has prescribed Galois module structure

Number Theory 2025-07-18 v1

Authors: Manabu Ozaki

Abstract

For any finite cyclic $p$ -group $G$ , we will show that every $\mathbb{Z}_p$ -torsion free finitely generated $\mathbb{Z}_p[G]$ -module appears as $\mathcal{O}_K^\times\otimes_{\mathbb{Z}}\mathbb{Z}_p$ up to $\mathbb{Z}_p[G]$ -free direct summands for a certain $G$ -extension $K/k$ of number fields.

Keywords

cyclic p-extension number fields Galois module structure unit group Z_p-module torsion-free finite cyclic p-group Galois extension

Cite

@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}
}

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