Serre subcategories and local cohomology

Let R be a commutative noetherian ring, let a be an ideal of R; and let S be a subcategory of the category of R-modules. In this paper, we define and study the class Sa consisting of all modules satisfying the condition Ca. If a and b are ideals of R, we get a necessary and su cient condition in order that S satisfies the conditions Ca and Cb simultaneously. We also find some su cient conditions under which S satisfies Ca. We investigate when local cohomology modules lie in a Serre subcategory.