Almost rational torsion points on elliptic curves

Frank Calegari

Let $A/\Bbb Q$ be an Abelian Variety. Let $P$ be a torsion point on $A$. Then $P$ is an \emph{almost rational torsion point} if it has the following property: Any two non-trivial Galois conjugates $\sigma P$, $\tau P$ of $P$ have sum different from $2P$. In this talk, we explain the connection between almost rational torsion points and the Manin-Mumford conjecture, and we classify almost rational torsion points on semistable elliptic curves.