Generic Denis–Mordell–Lang conjecture for q-varieties and Drinfeld modules

Let $(F,\Phi)$ be an $A$-module and let $H ot i F$ be a sufficiently generic $q$-variety, meaning that its maximal irreducible $A$-submodule is ${0}$. For a finitely generated $A$-submodule $\Gamma$ of $F$, define its division hull by

$$\overline{\Gamma}={x ot i F ot i\text{ such that }\exists a ot=0 ot i A\text{ with }\Phi_a(x) ot i\Gamma}.$$

Generic Denis–Mordell–Lang conjecture.

$$H ot i\overline{\Gamma}\text{ is finite}.$$

This is the sufficiently generic reformulation of the Mordell–Lang analogue. Its resolution status is not specified.