Denote by A := F q [T] and k := F q (T). Let φ be a Drinfeld A-module defined on the algebraic closure of k and h its canonical height. Let K/k be a finite extension and L/K a infinite Galois extension. By analogy with the terminology used by E. Bombieri and U. Zannier, we state that L has the property (B,φ) if exists a strictly positive constant which bound h on L except for torsion points of φ. S. David and A. Pacheco have proven that for all Drinfeld modules φ, the abelian closure of K has the property (B,φ). In this thesis we generalize this result, for the Drinfeld modules with complex multiplication.
Bogomolov Property for Drinfeld Modules with Complex Multiplications