Lemma 47.16.10. Let $(A, \mathfrak m, \kappa )$ be a Noetherian local ring with normalized dualizing complex $\omega _ A^\bullet $. Let $f \in \mathfrak m$ be a nonzerodivisor. Set $B = A/(f)$. Then there is a distinguished triangle
\[ \omega _ B^\bullet \to \omega _ A^\bullet \to \omega _ A^\bullet \to \omega _ B^\bullet [1] \]
in $D(A)$ where $\omega _ B^\bullet $ is a normalized dualizing complex for $B$.
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