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Sep 12, 2010 at 14:58 comment added Karl Schwede I'm confused, I don't see why Laurent's example fails. You made the claim about ``if and only if''. He provided an example of an open surjective morphism $f : X \to S$ and a coherent sheaf $M$ such that $R^i M = 0$ for all $i$ but $M$ does \emph{not} satisfy your condition on the support.
Sep 12, 2010 at 13:36 history answered kaddar CC BY-SA 2.5