An Addendum to the elliptic torsion anomalous conjecture in codimension 2

Abstract

The torsion anomalous conjecture states that for any variety $V$ in an abelian variety there are only finitely many maximal $V$-torsion anomalous varieties. We prove this conjecture for $V$ of codimension 2 in a product $E^N$ of an elliptic curve $E$ without CM, complementing previous results for $E$ with CM. We also give an effective upper bound for the normalized height of these maximal $V$-torsion anomalous varieties.