Definition 15.91.4. Let $A$ be a ring. Let $K \in D(A)$. Let $I \subset A$ be an ideal. We say $K$ is derived complete with respect to $I$ if for every $f \in I$ we have $T(K, f) = 0$. If $M$ is an $A$-module, then we say $M$ is derived complete with respect to $I$ if $M[0] \in D(A)$ is derived complete with respect to $I$.

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