I am interested in the following question: for $f$ being a morphism of schemes, which conditions ensure that $Rf^*_{et}$ is conservative? This is true if $f$ has a section or if $f$ is an \'etale covering; so this is also true for any smooth surjective $f$. Could I say that this statement is well-known?:) Is there a canonical reference for this fact (or for any its nice generalization?)? Actually, I would also like to apply this statement for a pro-smooth surjective $f$; are there any nice references for the properties of such morphisms?

Upd. Thank you very much for the comments; it was silly for me to forget about surjectivity.

loc. cit.). The statement at the level of derived categories follows immediately from there, because the functors of type $f^\star$ are exact. I don't see why being étale or smooth implies the property you want. – Denis-Charles Cisinski Mar 16 '11 at 21:39