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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.NT2024
A note on local formulae for the parity of Selmer ranks
Adam Morgan
In this note, we provide evidence for a certain twisted version of the parity conjecture for Jacobians, introduced in prior work of V. Dokchitser, Green, Konstantinou and the autho…
math.NT2024
Hasse principle for Kummer varieties in the case of generic 2-torsion
Adam Morgan
Conditional on finiteness of relevant Shafarevich--Tate groups, Harpaz and Skorobogatov used Swinnerton-Dyer's descent-fibration method to establish the Hasse principle for Kummer…