  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.
