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unige:12199 
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Weights in cohomology and the Eilenberg-Moore spectral sequence |
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| 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 sequence — weight filtration — equivariant cohomology — intersection cohomology — complex algebraic G–varieties | |
| Identifiers | DOI: 10.5802/aif.2109 arXiv: math/0405589v3 | |
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| Citation (ISO format) | 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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