The standard filtration on cohomology with compact supports with an appendix on the base change map and the Lefschetz hyperplane theorem

摘要

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