On the support of general local cohomology modules and filter regular sequences

Abstract

Let R be a commutative Noetherian ring with non-zero identity and a an ideal of R. In the present paper, we examine the question whether the support of H a n (N, M) must be closed in Zariski topology, where H a n (N, M) is the nth general local cohomology module of finitely generated R-modules M and N with respect to the ideal a.