In editing the algebraic geometry notes posted here, prompted by Brian Conrad, I am introducing the notion of radicial morphism. This seems to me to not be a notion that absolutely everyone should see in a first serious schemes course, given the volume of definitions a student must digest (even if this idea is wafer-thin). So I would like to make clear to the learner who this notion is for. But the problem is: I don't know. I have two bits of data: I've never used it professionally, and I know some arithmetic geometers (e.g. in my department) have used it. Thus I ask:
Who uses radicial morphisms?
In the answers, I expect to hear multiple interesting answers to the implicit question:
What are radicial morphisms good for?