Leif Melkersson: Finiteness properties of (local cohomology modules) with support at a closed set of dimension one.

The local cohomology modules   with respect to a maximal ideal, of a finitely generated module have good properties, they are namely artinian modules .In general  local cohomology modules with respect to an arbitrary ideal can be very bad. Hoewever when the ideal is one-dimensional they have good finiteness properties .  First we show that the category of modules cofinite with respect to a fixed one-dimensional ideal is a full abelian subcategory of the category of modules.