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I want to follow up a question from here (how to deduce version 1.a. from version 1). I know a version of decomposition theorem BBD: Version 1. Let $f:X\to Y$ be a (surjective) proper map of complex ...

This question is basically about comparison of IC sheaves (or their sheaf cohomologies) for the settings: 1. variety is over $\mathbb{C}$ and sheaf is $\mathbb{C}$-linear, 2. variety is over a finite ...

I have a few questions relating to the BBD decomposition theorem. I have come across the following two versions of the decomposition theorem. Version 1. Let $f : X \to Y$ be a proper map of ...