Lemma 49.2.3. Let $A \to B$ be a quasi-finite map of Noetherian rings.

If $A \to B$ factors as $A \to A_ f \to B$ for some $f \in A$, then $\omega _{B/A} = \omega _{B/A_ f}$.

If $g \in B$, then $(\omega _{B/A})_ g = \omega _{B_ g/A}$.

If $f \in A$, then $\omega _{B_ f/A_ f} = (\omega _{B/A})_ f$.

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