Čech cohomology

Summary

Čech cohomology computes cohomology of a sheaf from an open cover. It uses the sections of the sheaf on the open sets of the cover and on their finite intersections. It is defined by an explicit cochain complex, so it is often the practical way to compute sheaf cohomology. For a quasi-coherent sheaf on a separated scheme and an affine open cover, Čech cohomology equals sheaf cohomology. The same idea applied to the nerve of a cover gives Čech cohomology of a topological space.