Lower bounds of certain general local cohomology modules

Let R be a commutative Noetherian ring, a system of ideals of R, M an arbitrary R-module and t a non-negative integer. Let be a Melkersson subcategory of R-modules. Among other things, we prove that if is in for all i < t then is in for all i < t and for all If is the class of R-modules N with where is an integer, then is in for all i < t if (and only if) is in for all i < t and for all As consequences we study and compare vanishing, Artinianness and support of general local cohomology and ordinary local cohomology supported at ideals of its system of ideals at initial points i < t. We show that is not necessarily finite whenever is local and M a finitely generated R-module. Communicated by Ellen Kirkman