VIADA E.

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...

The Torsion Anomalous Conjecture states that an irreducible variety V embedded in a semi-abelian variety contains only finitely many maximal V -torsion anomalous varieties. In this paper we consider an irreducible variety embedded in a product of elliptic curves. Our main result provides a totally explicit bound for the Néron-Tate height of all...

We prove a sharp lower bound for the essential minimum of a nontranslate variety in certain abelian varieties. This uses and generalises a result of Galateau. Our bound is a new step in the direction of an abelian analogue by David and Philippon of a toric conjecture of Amoroso and David and has applications in the framework of anomalous intersections.

In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on curves of quite general shape and increasing genus. The method bases on some explicit and sharp estimates for the height of such rational points, and the bounds are...