Displaying similar documents to “Smith theory for algebraic varieties.”

Weights in the cohomology of toric varieties

Andrzej Weber (2004)

Open Mathematics

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We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complexIH T*(X)⊗H*(T). We also describe the weight filtration inIH *(X).

Weights in cohomology and the Eilenberg-Moore spectral sequence

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 * ( X ) is pure. This is the case, for example, if X is smooth and has only finitely many orbits. We work...

Double complexes and vanishing of Novikov cohomology

Hüttemann, Thomas (2011)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15. We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new...

Local cohomology multiplicities in terms of étale cohomology

Manuel Blickle, Raphaël Bondu (2005)

Annales de l'institut Fourier

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Using a recently introduced correspondence of Emerton-Kisin we give a description of Lyubeznik’s local cohomology invariants in terms of local étale cohomology with 𝐙 / p 𝐙 coefficients.