Abstract
Let
f:X−−>Y
be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups
f
∗
:I
H
∗
(Y)−−>I
H
∗
(X)
compatible with the induced homomorphism on cohomology. The crucial point in the argument is reduction to the finite characteristic. We give an alternative and short proof of the existence of a homomorphism
f
∗
. Our construction is an easy application of the Decomposition Theorem.