2006/05/23 by Hanamura, Masaki, Saito, Morihiko
#14F43 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.math/0605603
We show that the etale cohomology (with compact supports) of an algebraic variety X over an algebraically closed field has the canonical weight filtration W, and prove that the middle weight part of the cohomology with compact supports of X is a subspace of the intersection cohomology of a compactification X' of X, or equivalently, the middle weight part of the (so-called) Borel-Moore homology of X is a quotient of the intersection cohomology of X'. We are informed that this has been shown by A. Weber in the case X is proper (and k=\bC) using a theorem of G. Barthel, J.-P. Brasselet, K.-H. Fieseler, O. Gabber and L. Kaup on morphisms between intersection complexes. We show that the assertion immediately follows from Gabber's purity theorem for intersection complexes.