For a sheaf E of abelian groups on a topological space X, the sheaf cohomology groups Hi(X,E) for integers i are defined as the right derived functors of the functor of global sections, E ↦ E(X).
If E is a sheaf of OX-modules on a scheme X, then the cohomology groups Hi(X,E) (defined using the underlying topological space of X) are modules over the ring O(X) of regular functions.