en
Scientific article
Open access
English

Weights in cohomology and the Eilenberg-Moore spectral sequence

Published inAnnales de l'Institut Fourier, vol. 55, no. 2, p. 673-691
Publication date2005
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
Classification
  • 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
Updates (1)
Article
accessLevelPublic
Identifiers
ISSN of the journal0373-0956
665views
274downloads

Technical informations

Creation10/20/2010 8:53:00 AM
First validation10/20/2010 8:53:00 AM
Update time03/14/2023 4:07:51 PM
Status update03/14/2023 4:07:51 PM
Last indexation08/28/2023 7:51:17 PM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack