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Weights in cohomology and the Eilenberg-Moore spectral sequence

Weber, Andrzej
Published in Annales de l'Institut Fourier. 2005, vol. 55, no. 2, p. 673-691
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 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.
Keywords Eilenberg–Moore spectral sequenceweight filtrationequivariant cohomologyintersection cohomologycomplex algebraic G–varieties
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FRANZ, Matthias, WEBER, Andrzej. Weights in cohomology and the Eilenberg-Moore spectral sequence. In: Annales de l'Institut Fourier, 2005, vol. 55, n° 2, p. 673-691. https://archive-ouverte.unige.ch/unige:12199

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Deposited on : 2010-10-21

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