Leray's theorem

In algebraic geometry, Leray's theorem relates abstract sheaf cohomology with Čech cohomology.

Let F be a sheaf on a topological space X and U an open cover of X . If F is acyclic on every finite intersection of elements of U , then

where H ˇ q ( U , F ) is the q -th Čech cohomology group of F with respect to the open cover U .