Minoration effective de la hauteur des points d'une courbe de $G_m^2$ définie sur $Q$

Corentin Pontreau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We are concerned here with Lehmer's problem in dimension $2$~; we give a lower bound for the height of a non-torsion point of $G_m^2$ on a non-torsion curve defined over $Q$, depending on the degree of the curve only. We have first been inspired by~\cite{Am-Da3}; we develop a new approach, inherent in the dimension two (or more precisely the codimension two), and then obtain a better result where the error's term is improved significantly, moreover we give an explicit expression for the constant.

Mots clés: hauteur normalisée; géométrie diophantienne

Domaines: Théorie des nombres [math.NT]

Corentin Pontreau. Minoration effective de la hauteur des points d'une courbe de $G_m^2$ définie sur $Q$. 2005. ⟨hal-00008554⟩