3 papers
math.NT2026
Visible 2-torsion in the Tate-Shafarevich group of an elliptic curve
Tom Fisher
We show that every pair of 2-torsion elements in the Tate-Shafarevich group of an elliptic curve are visible in the same abelian surface. This was previously only known for a singl…
math.NT2023
Minimisation of 2-coverings of genus 2 Jacobians
Tom Fisher, Mengzhen Liu
An important problem in computational arithmetic geometry is to find changes of coordinates to simplify a system of polynomial equations with rational coefficients. This is tackled…
math.NT2022
Arbitrarily large -torsion in Tate-Shafarevich groups
E. Victor Flynn, Ari Shnidman
We show that, for any prime , there exist absolutely simple abelian varieties over with arbitrarily large -torsion in their Tate-Shafarevich group. To prove this…