  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
but no longer compatible with the present results.
