I was trying to understand the fppf topology for schemes and I found this question.
Consider any base scheme $S$ and let $G$ be a commutative $S$-group scheme locally (for the étale topology on $S$) free and finite. Consider the multiplication by $p$. Is it true that there exists a faithfully flat base change $S^{\prime}\rightarrow S$ such that the base change of the multiplication by $p$ is an epimorphism for the fppf topology, i.e. a faithfully flat morphism? Is it important to consider multiplication by $p$ or can we argue the same for some particular classes of maps?
I don't have any idea of how to discuss such kind of problems!
Thanks for any suggestion!