Scientific article
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Weights in cohomology and the Eilenberg-Moore spectral sequence

Published inAnnales de l'Institut Fourier, vol. 55, no. 2, p. 673-691
Publication date2005

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
  • arxiv : math.AG
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. doi: 10.5802/aif.2109
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ISSN of the journal0373-0956

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