Minoration de la hauteur canonique pour les modules de Drinfeld \`a multiplications complexes

Abstract

Lower Bound for the Canonical Height for Drinfeld Modules with Complex Multiplication. Let K be a fi nite extension of Fq(T), let L=K be a Galois extension with Galois group G and let E be the sub eld of L fixed by the center of G. Assume that there exists a finite place v of K such that the local degrees of E=K above v are bounded. Let $\phi$ be a Drinfeld module with complex multiplication. We give an e fective lower bound for the canonical height of $\phi$ on L outside the torsion points of $\phi$ . In the number field case, this problem was solved by F. Amoroso, S. David and U. Zannier.