Remark 10.65.6. Let $R \to S$ be a ring map. Let $N$ be an $S$-module. Let $\mathfrak p$ be a prime of $R$. Then
\[ \text{Ass}_ S(N \otimes _ R \kappa (\mathfrak p)) = \text{Ass}_{S/\mathfrak pS}(N \otimes _ R \kappa (\mathfrak p)) = \text{Ass}_{S \otimes _ R \kappa (\mathfrak p)}(N \otimes _ R \kappa (\mathfrak p)). \]
The first equality by Lemma 10.63.14 and the second by Lemma 10.63.16 part (1).
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