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papers

Publications (22)

math.NT2026

Hasse principle for intersections of two quadrics via Kummer surfaces

Adam Morgan, Alexei N. Skorobogatov

We prove new cases of the Hasse principle for Kummer surfaces constructed from 2-coverings of Jacobians of genus 2 curves, assuming finiteness of relevant Tate-Shafarevich groups.…

math.NT2017

Semistable types of hyperelliptic curves

Tim Dokchitser, Vladimir Dokchitser, Celine Maistret +1

In this paper, we explore three combinatorial descriptions of semistable types of hyperelliptic curves over local fields: dual graphs, their quotient trees by the hyperelliptic inv…

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.NT2021

On 2-Selmer groups of twists after quadratic extension

Adam Morgan, Ross Paterson

Let $E / Q$ be an elliptic curve with full rational 2-torsion. As d varies over squarefree integers, we study the behaviour of the quadratic twists $E_{d}$ over a fixed quadra…

math.NT2022

A note on hyperelliptic curves with ordinary reduction over 2-adic fields

Vladimir Dokchitser, Adam Morgan

We study a class of semistable ordinary hyperelliptic curves over 2-adic fields and the special fibre of their minimal regular model. We show that these curves can be controlled us…

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…