Henri Johnston

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math.NT2026

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.NT2026

Determination of the stably free cancellation property for orders

Werner Bley, Tommy Hofmann, Henri Johnston

Let $K$ be a number field, let $A$ be a finite-dimensional semisimple $K$ -algebra, and let $I^$ be an $O_{K}$ -order in $A$ . We give practical algorithms that determine wh…

math.NT2024

An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications

Henri Johnston, Andreas Nickel

Let $p$ be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for every admissible one-dimensional $p$ -adic Lie extensi…

math.NT2024

On the existence of free sublattices of bounded index and arithmetic applications

Henri Johnston, Alex Torzewski

Let $O$ be a Dedekind domain whose field of fractions $K$ is a global field. Let $A$ be a finite-dimensional separable $K$ -algebra and let $I^$ be an $O$ -order…

math.NT2024

Arakelov class groups of random number fields

Alex Bartel, Henri Johnston, Hendrik W. Lenstra

The main purpose of the paper is to formulate a probabilistic model for Arakelov class groups in families of number fields, offering a correction to the Cohen--Lenstra--Martinet he…