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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.

flag	asked Oct 4 2010 at 18:32 Makhalan Duff 3,837●5●36

jlk · Answer 1 · 2010-10-05 01:33:24Z UTC

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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.

edited Oct 5 2010 at 1:33

answered Oct 4 2010 at 21:42

jlk
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@BCnrd: Thanks for pointing this out. Edited to make my meaning more clear. – jlk Oct 5 2010 at 1:32

Relative Jacobian condition

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