I would like to know a list of properties that are known to lift up along an etale morphism. That is, given a ring $R$ with some property $P$, and an etale morphism $A\rightarrow B$, what properties of $A$ can be lifted up to $B$? What about the vice-versa?
For me, an etale map is a finite type flat map with vanishing module of differentials, that is: a finite type flat unramified map.
More than anything, I would like to find a reference that discusses such things. Possibly something more friendly than EGA4 and written in the language of commutative algebra rather than schemes. Strangely enough, I did not find much on stacksproject about this stuff..