Weights in cohomology and the Eilenberg-Moore spectral sequence

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

2004-05-31

arxiv.org/abs/math/0405589v3

Ann. Inst. Fourier 55, No.2, 673-691 (2005).

Mathematics

Algebraic Geometry

17 pages, final version, to appear in Annales de l'Institute Fourier

Scientific paper

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.

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