an arbitrary ${{\mathbb{F}}}_q$-scheme $S$. Roughly speaking, a smooth $V$- fern over $S$ is a flat family over $S$ of objects of the type in Definition \[smoothferndef\]. One can show the following with relative ease:[^1]

\[smoothferns0\]The scheme $\OV$ represents the functor that associates to an ${{\mathbb{F}}}_q$-scheme $S$ the set of isomorphism classes of smooth $V$-ferns over $S$.

While the notion of a smooth $V$-fern makes sense over any ${{\mathbb{F}}}_q$-scheme, Drinfeld modules of generic characteristic only occur over ${{\mathbb{F}}}_q(t)$-schemes. To generalize the equivalence between smooth $V$-ferns over $K$ and Drinfeld ${{\mathbb{F}}}_q[t]$-modules of rank $n$ and level $(t)$ over $K$, we must restrict ourselves to base schemes defined over $\Spec({{\mathbb{F}}}_q(t))$. However, we only restricted ourselves to Drinfeld modules of generic characteristic for simplicity. In fact, one may drop the requirement that the Drinfeld module be of generic characteristic, instead requiring that the characteristic of the Drinfeld module does not divide $(t)$. One then gets an equivalence for base schemes defined over $\Spec({{\mathbb{F}}}_q[t,t^{-1}])$. One can go even further and generalize the notion of level structure to that of a *Drinfeld level structure* (see, for instance, [@Del-Hu Definition 6.1]). This allows one to define Drinfeld modules of rank $n$ and level $(t)$ over arbitrary ${{\mathbb{F}}}_q[t]$-schemes, 