= Acyclic resolution theorem
{title2=$H^q(X,\mathcal F)\cong H^q(\Gamma(X,\mathcal I^\bullet))$}
If $0\to\mathcal F\to\mathcal I^0\to\mathcal I^1\to\cdots$ is an exact resolution of <sheaves> and each $\mathcal I^j$ has vanishing positive <sheaf cohomology>, then the cohomology of its global-section complex computes $H^q(X,\mathcal F)$. <Fine sheaves> provide acyclic terms on a paracompact manifold, giving the analytic <Dolbeault resolution of holomorphic differential forms>.
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