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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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