The Stacks project

Definition 10.65.2. Let $R \to S$ be a ring map. Let $N$ be an $S$-module. The relative assassin of $N$ over $S/R$ is the set

\[ \text{Ass}_{S/R}(N) = \{ \mathfrak q \subset S \mid \mathfrak q \in \text{Ass}_ S(N \otimes _ R \kappa (\mathfrak p)) \text{ with }\mathfrak p = R \cap \mathfrak q\} . \]

This is the set named $A$ in Lemma 10.65.1.

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View Definition 10.65.2 as pdf