Acyclic cover
= Acyclic cover
An open cover is acyclic for a specified <sheaf> if its restriction to every nonempty finite intersection has zero higher <sheaf cohomology>. The <acyclic cover theorem> then identifies the cover's <Čech cohomology> with sheaf cohomology. On a <separated scheme>, an affine open cover is acyclic for every <quasi-coherent sheaf>.