M. Ozaki

activity

20062026

most citedOn the Z_p-ranks of tamely ramified Iwasawa modules

12 citations · 13 across the 10 of their papers we have counts for

collaborators

10 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…

math.NT2023★ 1 cited

On the $p$ -adic limit of class numbers along a pro- $p$ -extension

Manabu Ozaki

Let $K / k$ be a pro- $p$ -extension over a number field $k$ whose Galois group is finitely generated and $k_{0} \subseteq k_{1} \subseteq \dots \subseteq k_{n} \subseteq \dots$ an ascending seq…

math.NT2023

A number field analogue of Weil's theorem on congruent zeta functions

Manabu Ozaki

Let $K$ be a function field of one variable over a finite field $F$ . Weil's celebrated theorem states that the congruent zeta function of $K / F$ is determined by t…

math.NT2013

On the abelian groups which occur as Galois cohomology groups of global unit groups

Manabu Ozaki

For any finite group G and integer i, let $H^{i} (G)$ be the set of all the isomorphism classes of the Galois cohomology groups $H^^{i} (K / k, E_{K})$ , where K/k runs over all…

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

On the p-adic limit of class numbers along a pro-p-extension

A number field analogue of Weil's theorem on congruent zeta functions

On the abelian groups which occur as Galois cohomology groups of global unit groups

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

On the $p$ -adic limit of class numbers along a pro- $p$ -extension