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Mar 14, 2015 at 20:28 comment added Daniel Juteau @PeterMcNamara Ok this was 5 years ago, but for the record (if someones happens to read this), I agree with Geordie: if you start with an IC which is not concentrated in one degree, then the direct image doesn't need to be perverse, even if the morphism is semi-small. You need a stronger condition like "stratified semi-small" (one can find the right condition by trying to prove that the direct image is perverse)...
Oct 22, 2009 at 22:26 comment added Ilya Nikokoshev Yes, it's a wonderful article, highly recommended to everyone.
Oct 22, 2009 at 0:44 comment added Peter McNamara My intention was to remain in the case of a semismall map (I've edited the question) where the direct image of a perverse sheaf is perverse.
Oct 21, 2009 at 17:01 history answered Geordie Williamson CC BY-SA 2.5