Displaying similar documents to “On the de Rham cohomology of algebraic varieties”

Duality for the de Rham cohomology of an abelian scheme

Robert F. Coleman (1998)

Annales de l'institut Fourier

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In this paper the equality is established of three different pairings between the first de Rham cohomology group of an abelian scheme over a base flat over ℤ and that of its dual. These pairings have appeared and been used either explicitly or implicitly in the literature. In the last section we deduce a generalization to arbitrary characteristic of Serre’s formula for the Poincaré pairing on the first de Rham cohomology group of a curve over a field of characteristic zero. ...

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...