Lemma 47.16.9. Let $(A, \mathfrak m, \kappa )$ be a Noetherian local ring with normalized dualizing complex. Let $I \subset \mathfrak m$ be an ideal of finite length. Set $B = A/I$. Then there is a distinguished triangle
in $D(A)$ where $E$ is an injective hull of $\kappa $ and $\omega _ B^\bullet $ is a normalized dualizing complex for $B$.