Problème de Lehmer pour les hypersurfaces de variétés abéliennes de type C.M

Details Problème de Lehmer pour les hypersurfaces de variétés abéliennes de type C.M Problème de Lehmer pour les hypersurfaces de variétés abéliennes de type C.M

2003-07-08

arxiv.org/abs/math/0307095v1

Mathematics

Number Theory

23 pages

Scientific paper

We obtain a lower bound for the normalised height of a non-torsion hypersurface $V$ of a C.M. abelian variety $A$ which is a refinement of a precedent result. This lower bound is optimal in terms of the geometric degree of $V$, up to an absolute power of a ``log'' (independant of the dimension of $A$). We thus extend the results of F. Amoroso and S. David on the same problem on a multiplicative group $\mathbb{G}_m^n$. When $A$ is an elliptic curve and $V=\bar{P}$ is the set of conjugates of a non torsion $\bar{k}$-point, we reobtain the result of M. Laurent on the elliptic Lehmer's problem.

Affiliated with

Also associated with

No associations

Rating

Problème de Lehmer pour les hypersurfaces de variétés abéliennes de type C.M 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 Problème de Lehmer pour les hypersurfaces de variétés abéliennes de type C.M, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Problème de Lehmer pour les hypersurfaces de variétés abéliennes de type C.M will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-10773