Definition 86.4.1. Let $A$ be a Noetherian ring and let $I \subset A$ be an ideal. Let $B$ be an object of (86.2.0.2). We say $B$ is *rig-smooth over $(A, I)$* if there exists an integer $c \geq 0$ such that $I^ c$ annihilates $\mathop{\mathrm{Ext}}\nolimits ^1_ B(\mathop{N\! L}\nolimits _{B/A}^\wedge , N)$ for every $B$-module $N$.

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