De Rham-Weil theorem

In algebraic geometry, 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.