Bulletin of the
Korean Mathematical Society BKMS

Let $R$ be a commutative Noetherian ring, $I$ an ideal of $R$ and $T$ be a non-zero $I$-cofinite $R$-module with $\dim(T)\leq 1$. In this paper, for any finitely generated $R$-module $N$ with support in $V(I)$, we show that the $R$-modules $\Ext^i_R(T,N)$ are finitely generated for all integers $i\geq 0$. This immediately implies that if $I$ has dimension one (i.e., $\dim R/I=1$), then ${\rm Ext}^i_R(H^{j}_{I}(M),N)$ is finitely generated for all integers $i,j\geq0$, and all finitely generated $R$-modules $M$ and $N$, with $\Supp(N)\subseteq V(I)$.

Keywords: arithmetic rank, cofinite modules, local cohomology, minimax modules

MSC numbers: 13D45, 14B15, 13E05