Local cohomology and Serre subcategories

The membership of the local cohomology modules of a module M in certain Serre subcategories of the category of modules is studied from below (in). Generalizations of depth and regular sequences are defined. The relation of these notions to local cohomology are found. It is shown that the membership of the local cohomology modules of a finite module in a Serre subcategory in the upper range just depends on the support of the module.