Mathematics – Number Theory
Scientific paper
2012-04-06
Mathematics
Number Theory
44 pages
Scientific paper
A 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 dense in V. We prove some cases of this conjecture. In particular we prove that if V is a weak-transverse translate in an abelian variety, then there are no V-torsion anomalous varieties. With a totally effective method, we also show that the V-torsion anomalous varieties of relative codimension one are non-dense in any weak-transverse variety V in a product of elliptic curves with CM. As an immediate consequence we prove that if V is a weak-transverse variety of codimension 2 in a product of CM elliptic curves, then V^ta is open dense in V. We also point out some implications on the effective Mordell-Lang Conjecture.
Checcoli Sara
Veneziano Francesco
Viada Evelina
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