On torsion anomalous intersections (with an appendix by P. Philippon)

Details On torsion anomalous intersections (with an appendix by P. Philippon) On torsion anomalous intersections (with an appendix by P. Philippon)

2012-04-06

arxiv.org/abs/1204.1435v2

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.

Affiliated with

Also associated with

No associations

Rating

On torsion anomalous intersections (with an appendix by P. Philippon) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On torsion anomalous intersections (with an appendix by P. Philippon), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On torsion anomalous intersections (with an appendix by P. Philippon) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-183488