A stupid question: which statements in section 5 of BBD will fail if we replace $\overline{\mathbb{Q}_l}$-sheaves by just $\mathbb{Q}_l$-ones? I am especially interested in Proposition 5.1.15.

BBD = Beilinson A., Bernstein J., Deligne P., Faisceaux pervers, Asterisque 100, 1982, 5-171.