= Vanishing of quasi-coherent cohomology on an affine scheme
{title2=$H^{i>0}(\operatorname{Spec}A,\widetilde M)=0$}
Every <quasi-coherent sheaf> on an <affine scheme> has zero higher <sheaf cohomology>. Together with the equivalence between modules and quasi-coherent sheaves on an affine scheme, this makes <affine varieties> the basic acyclic pieces for computing cohomology. An affine <open cover> of a <separated scheme> has affine finite intersections, so the <acyclic cover theorem> identifies its <Čech cohomology> with sheaf cohomology.
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