Local cohomology
In algebraic geometry, local cohomology is an analog of relative cohomology. Alexander Grothendieck introduced it in seminars in Harvard in 1961 written up by Hartshorne (1967), and in 1961-2 at IHES written up as SGA2 - Grothendieck (1968), republished as Grothendieck (2005).
In the geometric form of the theory, sections ΓY are considered of a sheaf F of abelian groups, on a topological space X, with support in a closed subset Y. The derived functors of ΓY form local cohomology groups
For applications in commutative algebra, the space X is the spectrum Spec(R) of a commutative ring R (supposed to be Noetherian throughout this article) and the sheaf F is the quasicoherent sheaf associated to an R-module M, denoted by . The closed subscheme Y is defined by an ideal I. In this situation, the functor ΓY(F) corresponds to the annihilator
...
Wikipedia