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Weights in cohomology and the Eilenberg-Moore spectral sequence
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 -variety
( being a connected algebraic group) in terms of its equivariant
cohomology provided that is pure. This is the case, for example, if
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.Comment: 17 pages, final version, to appear in Annales de l'Institute Fourie
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