Theoreme de Dobrowolski-Laurent pour les extensions abeliennes sur une courbe elliptique a multiplication complexe
| dc.creator | Ratazzi, Nicolas | |
| dc.date | 2004-02-13 | |
| dc.date | 2004-02-16 | |
| dc.date.accessioned | 2026-07-07T05:05:25Z | |
| dc.date.available | 2026-07-07T05:05:25Z | |
| dc.description | Let E/K be an elliptic curve with complex multiplication and let $K^{ab}$ be the Abelian closure of $K$. We prove in this article that there exists a constant $c(E/K)$ such that : for all point $P\in E(\bar{K})-E_{tors}$, we have \[\hat{h}(P)\geq\frac{c(E/K)}{D}(\frac{\log \log 5D}{\log 2D})^{13},\] where $D=[K^{ab}(P):K^{ab}]$. This result extends to the case of elliptic curve s with complex multiplication the previous resultof Amoroso-Zannier \cite{AZ} on the analogous problem on the multiplicative group $\mathbb{G}_m$, and generalizes to the case of extensions of degree D the result of Baker \cite{baker} on the lower bound of the Néron-Tate height of the points defined over an Abelian extension of an elliptic curve with complex multiplication. This result also enables us to simplify the proof of a theorem of Viada \cite{viada}. | |
| dc.description | correction of a small LaTeX bug : the two last pages were unvoluntarily in Italics | |
| dc.identifier | https://arxiv.org/abs/math/0402224 | |
| dc.identifier | http://arxiv.org/abs/math/0402224 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70160 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G50; 14G40; 14K22 | |
| dc.title | Theoreme de Dobrowolski-Laurent pour les extensions abeliennes sur une courbe elliptique a multiplication complexe | |
| dc.type | text |