most recent 30 from http://mathoverflow.net 2013-05-24T14:33:55Z http://mathoverflow.net/feeds/question/58684 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/58684/when-inverse-image-is-conservative-a-reference-or-a-generalization Mikhail Bondarko 2011-03-16T20:21:44Z 2011-03-17T09:24:14Z

<p>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? </p> <p>Upd. Thank you very much for the comments; it was silly for me to forget about surjectivity.</p>