Lemma 15.94.7. Let $I$ be an ideal in a Noetherian ring $A$. Let ${}^\wedge $ denote derived completion with respect to $I$. Let $K \in D^-(A)$.

If $M$ is a finite $A$-module, then $(K \otimes _ A^\mathbf {L} M)^\wedge = K^\wedge \otimes _ A^\mathbf {L} M$.

If $L \in D(A)$ is pseudo-coherent, then $(K \otimes _ A^\mathbf {L} L)^\wedge = K^\wedge \otimes _ A^\mathbf {L} L$.

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