  M. Goresky, G. Harder, and R. MacPherson defined weighted cohomologies of
arithmetic groups \Gamma in a real group G, with coefficients in certain local
systems, associated to arbitrary upper and lower weight profiles. The author
shows, using essentially local arguments on the reductive Borel-Serre
compactification, that these cohomologies agree with certain weighted L^2
cohomologies defined by J. Franke. When the rank of G is equal to that of a
maximal compact subgroup, this implies that the cohomologies associated to both
upper and lower middle profiles are both isomorphic to L^2 cohomology.
