2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97896We 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.17 pages, final version, to appear in Annales de l'Institute FourierAlgebraic GeometryAlgebraic Topology32S35, 14L30, 14F43, 55N33text