The elliptic torsion anomalous conjecture in codimension 2
  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 any elliptic curve E. This was known only when E has CM. We also give an effective upper bound for the normalized height of these maximal V-torsion anomalous varieties. 
Patrik Hubschmid, Evelina Viada
math.NT