Cofiniteness of generalized local cohomology modules over local rings.

Let (R, 픪) be a local commutative Noetherian ring and I an ideal of R. Assume that M is a finitely generated R-module of finite projective dimension p and N is a finitely generated R-module of dimension d. We prove that H픪1(H Ip+d−1(M,N)) is Artinian. Moreover, if HomR(R/I,HIp+d−1(M,N)) is finitely generated, then HIp+d−1(M,N) is an I-cofinite R-module. [ABSTRACT FROM AUTHOR]