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Do you mean that you want a generalization of the Jacobian condition 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.

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Do you mean the Jacobian condition for smoothness of, say, a variety? If so, then the Néron Models book has a nice discussion of this in the section on smoothness.