A remark on local cohomology (Q1270083)

Let \(A\) be a commutative ring, \(M\) and \(A\)-module, \(\widetilde M\) the associated \({\mathcal O}_{\text{Spec}(A)}\)-module and \(I\) a finitely generated ideal of \(A\). The local cohomology groups \(H^n\) with respect to \(V(I) \subseteq \text{Spec}(A)\) are defined in the category of abelian sheaves. Using a generating set for \(I\) the author constructs a cohomological Koszul complex which leads to a functional equivalent characterization of \(H^n\) for all \(n\).