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Does anybody know references for perverse sheaves, especially the intermediate/middle extension functor for $\mathbf{Q}_\ell$-sheaves for varieties over (the algebraic closure of) finite fields, except

1) BBD, asterisque 100

2) Kiehl, Weissauer

I am mainly interested in the situation $j: U \hookrightarrow X$, $X/k$ smooth projective irreducible and want to understand the restriction of $j_{!*} B$ to the closed complement $X \setminus U$, especially its cohomology with respect to the standard t-structure. (I already know $i^{-1} j_{!*} B \in {}^p D^{\leq -1}(X \setminus U)$.)

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A great book which contains basic information about perverse sheaves (although not so much about the topics you are especially looking for) is

D-Modules, Perverse Sheaves, and Representation Theory

by Hotta, Takeuchi and Tanisaki. Its even available for free online:

http://www.math.harvard.edu/~gaitsgde/grad_2009/Hotta.pdf

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  • $\begingroup$ As alluded to in the answer, though, Hotta, Takeuchi, and Tanisaki do not discuss $\ell$-adic sheaves. In general, there seem to be far more references on this topic working over $\mathbb{C},$ probably because the topological intuitions are much clearer in this setting (and fewer prerequisites are necessary). $\endgroup$
    – Mike Skirvin
    Commented Oct 15, 2010 at 14:16

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