2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76296We 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.28 pages à paraître dans Acta ArithmeticaNumber TheoryAMS 2000: 11G50, 11J81, 14G40text