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Article Dans Une Revue Rendiconti Lincei. Matematica e Applicazioni Année : 2014

On torsion anomalous intersections

Sara Checcoli
Francesco Veneziano
  • Fonction : Auteur

Résumé

A deep conjecture on torsion anomalous varieties states that if $V$ is a weak-transverse variety in an abelian variety, then the complement $V^{ta}$ of all $V$-torsion anomalous varieties is open and dense in $V$. We prove some cases of this conjecture. We show that the $V$-torsion anomalous varieties of relative codimension one are non-dense in any weak-transverse variety $V$ embedded in a product of elliptic curves with CM. We give explicit uniform bounds in the dependence on $V$. As an immediate consequence we prove the conjecture for $V$ of codimension two in a product of CM elliptic curves. We also point out some implications on the effective Mordell-Lang Conjecture.

Dates et versions

hal-01625161 , version 1 (27-10-2017)

Identifiants

Citer

Sara Checcoli, Francesco Veneziano, Evelina Viada. On torsion anomalous intersections. Rendiconti Lincei. Matematica e Applicazioni, 2014, 25 (1), pp.1-36. ⟨10.4171/RLM/666⟩. ⟨hal-01625161⟩

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