$k$ is a field of characteristic $p$. $k[t]$ has canonical first-order differential operator $\partial$ As an endomorphism of $k[t]$, $\partial^p=0$. First way to fix it: Use the divided power ...
This question is inspired by an earlier one about the possibility of using the full ring of differential operators on a flag variety to develop a theory of localization in characteristic $p$. (Here ...