Suzanne O'Hara

Heavenly Elliptic Curves over Cubic Number Fields

The study of heavenly abelian varieties is motivated by a question of Ihara. When an elliptic curve $E/K$ is heavenly at $\ell$, the extension $K(E[\ell^\infty])/K(\mu_\ell^\infty)$ is pro-$\ell$ and unramified away from $\ell$. These are the same arithmetic conditions as the fixed field of the kernel attached to pro-$...