Fabio Ferri

activity

20182024

collaborators

5 papers

math.RA2024

On the number of quaternion and dihedral braces and Hopf--Galois structures

Nigel P. Byott, Fabio Ferri

We prove a conjecture of Guarnieri and Vendramin on the number of braces of a given order whose multiplicative group is a generalised quaternion group. At the same time, we give a…

math.NT2023

Applications of representation theory and of explicit units to Leopoldt's conjecture

Fabio Ferri, Henri Johnston

Let $L / K$ be a Galois extension of number fields and let $G = Gal (L / K)$ . We show that under certain hypotheses on $G$ , for a fixed prime number $p$ , Leopoldt's conjecture at…

math.NT2021

Leopoldt-type theorems for non-abelian extensions of Q

Fabio Ferri

We prove new results concerning the additive Galois module structure of certain wildly ramified finite non-abelian extensions of Q. In particular, when K/Q is a Galois extension wi…

math.NT2020

How far is an extension of $p$ -adic fields from having a normal integral basis?

Ilaria Del Corso, Fabio Ferri, Davide Lombardo

Let $L / K$ be a finite Galois extension of $p$ -adic fields with group $G$ . It is well-known that $O_{L}$ contains a free $O_{K} [G]$ -submodule of finite index. We stu…

math.NT2018

Tame Galois module structure revisited

Fabio Ferri, Cornelius Greither

A number field $K$ is Hilbert-Speiser if all of its tame abelian extensions $L / K$ admit NIB (normal integral basis). It is known that $Q$ is the only such field, but when…

On the number of quaternion and dihedral braces and Hopf--Galois structures

Applications of representation theory and of explicit units to Leopoldt's conjecture

Leopoldt-type theorems for non-abelian extensions of Q

How far is an extension of p-adic fields from having a normal integral basis?

Tame Galois module structure revisited

How far is an extension of $p$ -adic fields from having a normal integral basis?