# On torsion anomalous intersections

Abstract : 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.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-01625161
Contributor : Ariane Rolland <>
Submitted on : Friday, October 27, 2017 - 11:31:29 AM
Last modification on : Thursday, January 11, 2018 - 6:12:14 AM

### Identifiers

• HAL Id : hal-01625161, version 1

### Citation

Sara Checcoli, Francesco Veneziano, Evelina Viada. On torsion anomalous intersections. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni, European Mathematical Society, 2014, 25 (1), pp.1-36. ⟨hal-01625161⟩

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