finiteness properties of extension functors of generalized local cohomology modules

Let r be a commutative noetherian ring with non-zero identity, a an ideal of r, m and x finitely generated r-modules, and t a non-negative integer. in this paper, we demonstrate that if the generalized local cohomology modules hi a(m; x) are a-cofinite for all i < t, then the module ext1 r(r=a; ht a(m; x)) is finitely generated.