### ${L}^{2}$ -cohomology of locally symmetric varieties

Eduard Looijenga (1988)

Compositio Mathematica

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Eduard Looijenga (1988)

Compositio Mathematica

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Sascha Orlik (2001)

Annales scientifiques de l'École Normale Supérieure

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Annette Huber, Guido Kings (1999)

Annales scientifiques de l'École Normale Supérieure

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Matthias Franz, Andrzej Weber (2005)

Annales de l’institut Fourier

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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 ${H}_{G}^{*}\left(X\right)$ is pure. This is the case, for example, if $X$ is smooth and has only finitely many orbits. We work...

Jürgen Rohlfs, Birgit Speh (1987)

Annales scientifiques de l'École Normale Supérieure

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