# Relative Jacobian condition

This question is really elementary.

Where can I learn about the Jacobian condition not over a field?

I think I heard once that there's a Jacobian condition even for $f: X \rightarrow Y$. I'm not really sure what that would be, and what it would imply if it's satisfied, but I'd like some good references so I can learn.

-

## 1 Answer

Do you mean that you want a generalization of the Jacobian criteria for the smoothness of, say, a variety to the case of a morphism of schemes? If so, then the Néron Models book has a nice discussion of this in the section on smoothness.

-
@BCnrd: Thanks for pointing this out. Edited to make my meaning more clear. – jlk Oct 5 '10 at 1:32