##
Weights in cohomology and the
Eilenberg-Moore spectral sequence

**Matthias Franz, Andrzej Weber**

17 pages,

We show that in the category of complex algebraic varieties,
the Eilenberg-Moore spectral sequence can be endowed
with a weight filtration.
This implies that it degenerates if all involved spaces
have pure cohomology.
As application, we compute the rational cohomology of an algebraic
$G$-variety $X$
($G$ being a connected algebraic group)
in terms of its equivariant cohomology provided that $H_G(X)$ is pure.
This is the case, for example, if $X$ is
smooth and has only finitely many orbits.
We work in the category of mixed sheaves; therefore our results apply
equally to (equivariant) intersection homology.