The Stacks project

Definition 16.2.1. Let $R \to A$ be a ring map. The singular ideal of $A$ over $R$, denoted $H_{A/R}$ is the unique radical ideal $H_{A/R} \subset A$ with

\[ V(H_{A/R}) = \{ \mathfrak q \in \mathop{\mathrm{Spec}}(A) \mid R \to A \text{ not smooth at }\mathfrak q\} \]

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View Definition 16.2.1 as pdf