Sheaf cohomology

Summary

Sheaf cohomology assigns to a sheaf $\mathcal{F}$ on a space $X$ a sequence of groups $H^i(X, \mathcal{F})$, the right derived functors of the global sections functor. In algebraic geometry it is applied to sheaves of modules on schemes, above all to quasi-coherent and coherent sheaves. For these the groups are modules, and in good cases finite-dimensional vector spaces. It measures the failure of local sections to glue and of surjections of sheaves to be surjective on global sections. The topological side of the theory, with constant and locally constant coefficients, is described in sheaf cohomology in topology.