Let $\mathfrak{ a}$ be an ideal of a commutative noetherian ring $R$ and $M, N$ two finitely generated $R$-modules. By using a spectral sequence argument, it is shown that if either $\mathrm{ dim}_RM\leq2$ and $\mathrm{ H}^{ i}_\mathfrak{ a}(N)$ are $\mathfrak{ a}$-cofinite for all $i\geq0$, or $\mathrm{ H}^{ i}_\mathfrak{ a}(N)$ is an $\mathfrak{ a}$-cofinite module of dimension $\leq1$ for each $i\geq1$, or $q(\mathfrak{ a},R)\leq1$, then the $R$-modules $\mathrm{ H}^{ t}_\mathfrak{ a}(M,N)$ are $\mathfrak{ a}$-cofinite for all $t\geq0$.
Categories: math.AC