Local cohomology

Summary

Let $M$ be a module over a commutative Noetherian ring and let $I$ be an ideal. The local cohomology modules $H^i_I(M)$ are the right derived functors of the functor of sections supported on $I$. It was introduced by Grothendieck. Over a Noetherian local ring, local cohomology at the maximal ideal detects the depth and the Krull dimension of a finitely generated module. It is the subject of Grothendieck's local duality.