  We describe the standard and Leray filtrations on the cohomology groups with
compact supports of a quasi projective variety with coefficients in a
constructible complex using flags of hyperplane sections on a partial
compactification of a related variety. One of the key ingredients of the proof
is the Lefschetz hyperplane theorem for perverse sheaves and, in an appendix,
we discuss the base change maps for constructible sheaves on algebraic
varieties and their role in a proof, due to Beilinson, of the Lefschetz
hyperplane theorem.
