Lemma 47.16.2 (0A7N)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 47: Dualizing Complexes
Section 47.16: Dualizing complexes over local rings
Lemma 47.16.2 (cite)

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Lemma 47.16.2. Let $(A, \mathfrak m, \kappa )$ be a Noetherian local ring with normalized dualizing complex $\omega _ A^\bullet$ . Let $A \to B$ be surjective. Then $\omega _ B^\bullet = R\mathop{\mathrm{Hom}}\nolimits _ A(B, \omega _ A^\bullet )$ is a normalized dualizing complex for $B$ .

Proof. Special case of Lemma 47.16.1. $\square$

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