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

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

2009-01-06

arxiv.org/abs/0901.0660v1

Mathematics

Algebraic Geometry

Dedicated to A.J. Sommese on his 60th birthday

Scientific paper

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.

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