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

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

## Comments (0)

There are also: