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Nov 26, 2012 at 8:10 comment added Damian Rössler Also note that if you do not assume that $S$ is surjective, then any closed immersion gives a counterexample (Jason Starr's answer is a closed immersion but you can see that he assumed that you wanted the morphism to be surjective).
Nov 26, 2012 at 8:07 comment added Damian Rössler Note that this is true if $S$ is normal, by Zariski's main theorem.
Nov 25, 2012 at 21:39 answer added Ray Hoobler timeline score: 2
Nov 25, 2012 at 16:36 answer added Mohan timeline score: 3
Nov 25, 2012 at 1:57 vote accept HNuer
Nov 24, 2012 at 23:39 answer added Jason Starr timeline score: 9
Nov 24, 2012 at 23:08 history asked HNuer CC BY-SA 3.0