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Aug 9, 2015 at 17:39 comment added Tian An My mistake: I meant (1) and (3).
Aug 9, 2015 at 14:02 comment added Mikhail Bondarko Yet it seems that de Cataldo and Migliorini do not discuss Huber's weights.
Aug 9, 2015 at 4:10 comment added Tian An de Cataldo and Migliorini's survey paper "The Decomposition Theorem, perverse sheaves and the topology of algebraic maps" discuss (1) and (2), and contain many references that may be lead to something helpful.
Aug 8, 2015 at 11:08 history edited Mikhail Bondarko CC BY-SA 3.0
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Aug 8, 2015 at 10:44 history asked Mikhail Bondarko CC BY-SA 3.0