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math.NT2025
Non-Isomorphic Abelian Varieties with the Same Arithmetic
Jamie Bell
We construct two abelian varieties over which are not isomorphic, but have isomorphic Mordell--Weil groups over every number field, isomorphic Tate modules and equal v…
math.NT2024
A Note on the Growth of Sha in Dihedral Extensions
Jamie Bell
We provide a formula for the order of the Tate--Shafarevich group of elliptic curves over dihedral extensions of number fields of order , up to powers and primes divid…
math.NT2022
p-Selmer ranks of CM abelian varieties
Jamie Bell
For an elliptic curve with complex multiplication over a number field, the --Selmer rank is even for all . Česnavičius proved this using the fact that admits a $…