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 $i^{-1} j_{!*} B \in {}^p D^{\leq -1}(X \setminus U)$.)