De Rham–Weil theorem

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

Let F be a sheaf on a topological space X and F ∙ a resolution of F by acyclic sheaves. Then

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

The De Rham–Weil theorem follows from the more general fact that derived functors may be computed using acyclic resolutions instead of simply injective resolutions.

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