Weights in cohomology and the Eilenberg-Moore spectral sequence

Article Article scientifique Article Weights in cohomology and the Eilenberg-Moore spectral sequence eng 2005 author Franz Matthias 585980 author Weber Andrzej 673-691 10.5802/aif.2109 0373-0956 math/0405589v3 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. Eilenberg–Moore spectral sequence weight filtration equivariant cohomology intersection cohomology complex algebraic G–varieties Dewey 510 arxiv math.AG 25 Section de mathématiques 11 false Annales de l'Institut Fourier 55 2 2f419d12-fced-4f99-8460-b114a4d67ca7 Article Public math_0405589v3.pdf 234787 application/pdf openAccess Faculté des sciences / Section de mathématiques

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Weights in cohomology and the Eilenberg-Moore spectral sequence	Annales de l'Institut Fourier			2005	780	889

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Franz, Matthias