De Rham–Weil theorem

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In algebraic topology, the De Rham-Weil theorem allows computation of sheaf cohomology using an acyclic resolution of the sheaf in question.

Let \mathcal F be a sheaf on a topological space X and \mathcal F^\bullet a resolution of \mathcal F by acyclic sheaves. Then

H^q(X,\mathcal F) \cong H^q(\mathcal F^\bullet(X)),

where H^q(X,\mathcal F) denotes the q-th sheaf cohomology group of X with coefficients in \mathcal F.

This article incorporates material from De Rham-Weil theorem on PlanetMath, which is licensed under the GFDL.