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Sep 22, 2013 at 16:40 comment added Dan Petersen Unfortunately I can't include the proof now (I'm posting from my phone) but I'll do it later this evening.
Sep 22, 2013 at 16:35 comment added Dan Petersen Thanks a lot! In fact I think the proof I have is slightly simpler (it doesn't need perverse sheaves or the decomposition theorem), probably I should've included it in the original question.
Sep 22, 2013 at 11:44 history edited Geordie Williamson CC BY-SA 3.0
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Sep 22, 2013 at 11:14 history edited Geordie Williamson CC BY-SA 3.0
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Sep 22, 2013 at 10:31 comment added Geordie Williamson You are right, the problem is "the above remarks imply that $K$ is of weight $\ge 0$", in fact one only gets $K$ of wt $\ge -1$.
Sep 22, 2013 at 10:24 history edited Geordie Williamson CC BY-SA 3.0
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Sep 22, 2013 at 9:43 comment added Dan Petersen Thanks. But it seems you are not using the surjectivity hypothesis anywhere? The result is obviously false without it (think about a closed immersion).
Sep 22, 2013 at 9:09 history answered Geordie Williamson CC BY-SA 3.0