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Matthias Franz; Andrzej Weber
Weights in cohomology and the Eilenberg-Moore spectral sequence
(Poids dans la cohomologie et la suite spectrale d'Eilenberg-Moore)
Annales de l'institut Fourier, 55 no. 2 (2005), p. 673-691, doi: 10.5802/aif.2109
Article PDF | Reviews MR 2147902 | Zbl 02171520
Class. Math.: 32S35, 14L30, 14F43, 55N33
Keywords: Eilenberg-Moore spectral sequence, weight filtration, equivariant cohomology, intersection cohomology, complex algebraic $G$-varieties

Résumé - Abstract

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 spaces involved 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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