Acyclic cover theorem
= Acyclic cover theorem
{wiki=Leray's_theorem}
If every nonempty finite intersection of members of an open cover has vanishing higher <sheaf cohomology> for $\mathcal F$, then the cover's <Čech cohomology> computes $H^p(X,\mathcal F)$. An affine open cover of a separated scheme satisfies this condition for a quasi-coherent sheaf because its finite intersections are affine.