Definition 88.8.1. Let $A$ be a Noetherian ring and let $I \subset A$ be an ideal. Let $B$ be an object of (88.2.0.2). We say $B$ is *rig-étale over $(A, I)$* if there exists an integer $c \geq 0$ such that for all $a \in I^ c$ multiplication by $a$ on $\mathop{N\! L}\nolimits _{B/A}^\wedge $ is zero in $D(B)$.

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