Deux remarques sur le probleme de Lehmer sur les varietes abeliennes
| dc.creator | Ratazzi, Nicolas | |
| dc.date | 2004-02-13 | |
| dc.date.accessioned | 2026-07-07T05:05:26Z | |
| dc.date.available | 2026-07-07T05:05:26Z | |
| dc.description | Let $A/K$ be an abelian variety over a number field $K$. We prove in this article that a good lower bound (in terms of the degree $[K(P):K]$) for the Néron-Tate height of the points $P$ of infinite order modulo every strict abelian subvarieties of $A$ implies a good lower bound for the height of all the non-torsion points of $A$. In particular when $A$ is of C.M. type, a theorem of David and Hindry enables us to deduce, up to ``log'' factors, an optimal lower bound for the height of the non-torsion points of $A$. In the C.M. type case, this improves the previous result of Masser \cite{lettre}. Using the same theorem of David and Hindry we prove in the second part an optimal lower bound, up to ``log'' factors, for the product of the Néron-Tate height of $n$ End$(A)$-linearly independant non-torsion points of a C.M. type abelian variety. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0402225 | |
| dc.identifier | http://arxiv.org/abs/math/0402225 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70161 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G50, 14H52, 14K22, 11R18 | |
| dc.title | Deux remarques sur le probleme de Lehmer sur les varietes abeliennes | |
| dc.type | text |