Example 3

Let $\Omega$ be a dualizing A-module. For $i \neq \dim(A)$, one has $\mathrm{Ext}_A^i(A/\alpha, \Omega) = 0$ for every ideal of definition $\alpha$ of A (§ 8, No. 5, example 3), whence $H_A^i(\Omega) = 0$; for $i = \dim(A)$, the A-module $H_A^i(\Omega)$, which is isomorphic to $\varprojlim \mathrm{Ext}_A^i(A/\mathfrak{m}_A^n, \Omega)$, is a Matlis module (loc. cit., example 6).