On the finiteness properties of extension and torsion functors of local cohomology modules

Abstract

Let R R be a commutative Noetherian ring with non-zero identity, a \mathfrak {a} and b \mathfrak {b} ideals of R R with a ⊆ b \mathfrak {a} \subseteq \mathfrak {b} , and M M a finitely generated R R -module. In this paper, for fixed integers j j and n n , we study the finiteness of Ext R j ⁡ ( R / b , H a n ( M ) ) \operatorname {Ext}^j_R(R/\mathfrak {b},H^n_{\mathfrak {a}}(M)) and T o r j R ( R / b , H a n ( M ) ) Tor_j^R(R/\mathfrak {b},H^n_{\mathfrak {a}}(M)) in several cases.