A. Morgan

collaborators

3 papers

math.NT2025

Constructing Jacobians of rank 1

Peter Koymans, Adam Morgan

Let $K$ be a number field, let $g \geq 1$ be an integer and let $f (x) = (x - a_{1}) \dots (x - a_{2 g + 1}) \in O_{K} [x]$ be a polynomial that splits into $2 g + 1$ distinct linear fact…

math.NT2025

Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups

Alex Bartel, Adam Morgan

We address several seemingly disparate problems in arithmetic geometry: the statistical behaviour of the Galois module structure of Mordell--Weil groups of a fixed elliptic curve o…

math.NT2024

On Galois covers of curves and arithmetic of Jacobians

Alexandros Konstantinou, Adam Morgan

We study the arithmetic of curves and Jacobians endowed with the action of a finite group $G$ . This includes a study of the basic properties, as $G$ -modules, of their $ℓ$ -adic r…