The Stacks project

Lemma 38.13.4. Let $R \to S$ be a ring map which is essentially of finite type. Let $N$ be a localization of a finite $S$-module flat over $R$. Let $M$ be an $R$-module. Then

\[ \text{WeakAss}_ S(M \otimes _ R N) = \bigcup \nolimits _{\mathfrak p \in \text{WeakAss}_ R(M)} \text{Ass}_{S \otimes _ R \kappa (\mathfrak p)}(N \otimes _ R \kappa (\mathfrak p)) \]

Proof. This lemma is a translation of Lemma 38.13.3 into algebra. Details of translation omitted. $\square$

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