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Weights in cohomology and the Eilenberg-Moore spectral sequence. (English) Zbl 1145.14021
According to L. Smith [Bull. Am. Math. Soc. 75, 873–878 (1969; Zbl 0177.51403)] the entries of the Eilenberg-Moore spectral sequence are the cohomology groups with rational coefficients of certain topological spaces and the differentials are induced by the maps between them. The main objective of the paper under review is to show that Smith’s construction can be carried out in the derived category of sheaves on algebraic varieties. As a consequence the Eilenberg-Moore spectral sequence can be endowed with a weight filtration which extends the filtration constructed by P. Deligne.
The authors use the obtained results to study the weight structure in the (rational) cohomology and equivariant cohomology of algebraic \(G\)-varieties, where \(G\) is a linear algebraic group.

MSC:
14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
14L30 Group actions on varieties or schemes (quotients)
55N33 Intersection homology and cohomology in algebraic topology
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