M. Ozaki

collaborators

3 papers

math.NT2026

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

Takenori Kataoka, Manabu Ozaki

Let $G$ be a finite $p$ -group. We construct a $G$ -extension $K / k$ of number fields such that the $p$ -adic completion of the unit group of $K$ has a prescribed $Z_{p} [G]$ -mod…

math.NT2025

A number field analogue of the Grothendieck conjecture for curves over finite fields

Manabu Ozaki

In the present paper, we provide a new analogy between number fields and 1-dimensional function fields over finite fields from the viewpoint that the maximal cyclotomic extension o…

math.NT2025

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

Manabu Ozaki

For any finite cyclic $p$ -group $G$ , we will show that every $Z_{p}$ -torsion free finitely generated $Z_{p} [G]$ -module appears as $\mathcal{O}_K^\times\otimes_{\mathb…

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

A number field analogue of the Grothendieck conjecture for curves over finite fields

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

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

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