On the Torsion Anomalous Conjecture in CM abelian varieties

Sara Checcoli (1) , Evelina Viada (2)

1 IF - Institut Fourier
2 Department of Mathematics [Basel]

The Torsion Anomalous Conjecture (TAC) states that a subvariety V of an abelian variety A has only finitely many maximal torsion anomalous subvarieties. In this work we prove, with an effective method, some cases of the TAC when the ambient variety A has CM, generalising our previous results in products of CM elliptic curves. When V is a curve, we give new results and we deduce some implications on the effective Mordell-Lang Conjecture.

Domaines: Théorie des nombres [math.NT]

Sara Checcoli, Evelina Viada. On the Torsion Anomalous Conjecture in CM abelian varieties. Pacific Journal of Mathematics, 2014, 271 (2), pp.321-345. ⟨10.2140/pjm.2014.271.321⟩. ⟨hal-01625058⟩