We finally give some results in order to find a construction analogous to the one that has been built up by J. Pila and U. Zannier in their work. In the third section we prove our main result. In the fourth and last section we make some little consideration about our work.

We propose a lower bound estimate in Dobrowolski's form of the canonical height of a Drinfeld module having a positive density of supersingular primes. This estimate takes into account the inseparable case and it is given as a function of: the degree of the field of coefficients, the height of the module and its rank. We will show that the class of Drinfeld modules we consider includes all CM Drinfeld modules with rank either 1 or a prime number different from the field characteristic.

The aim of this work is to present a possible adaptation of the Manin-Mumford conjecture to the T −modules, a mathematical object which has been introduced in the 1980's by G. Anderson as the natural analogue of the abelian varieties in the context of modules over rings which are contained in positive characteristic function fields. We propose then a generalisation of such an adapted conjecture to a modified general version of Mordell-Lang conjecture for T −modules which might correct the one proposed for the first time by L. Denis in [Den2] but no longer compatible with the present results.We will remind in our first preliminary section the formulation of the Mordell-Lang and the Manin-Mumford conjectures and the definition of T −modules and sub-T −modules, listing nothing more than the basic definitions and properties which are strictly essential to us in order to state and prove our theorems. All the detailed informations the reader G. Faltings proved the Mordell-Lang conjecture (see [F]) in the following version.

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