Remark 1

When the $A$-module $M$ is finitely generated, the $\widehat{A}$-module $\mathrm{Ext}_A^{d-i}(M, \widehat{\Omega})$ is identified with $\widehat{A} \otimes_A \mathrm{Ext}_A^{d-i}(M, \Omega)$ ($A$, X, p. 108, Proposition 7, c)), and $\delta^i(M)$ can also be obtained by composing $D(\gamma^i(M))$ with the biduality isomorphism.