Lemma 59.76.6. Let $X$ be a scheme. Let $\Lambda $ be a Noetherian ring. Let $K, L \in D_ c^-(X_{\acute{e}tale}, \Lambda )$. Then $K \otimes _\Lambda ^\mathbf {L} L$ is in $D_ c^-(X_{\acute{e}tale}, \Lambda )$.
Lemma 59.76.6. Let $X$ be a scheme. Let $\Lambda $ be a Noetherian ring. Let $K, L \in D_ c^-(X_{\acute{e}tale}, \Lambda )$. Then $K \otimes _\Lambda ^\mathbf {L} L$ is in $D_ c^-(X_{\acute{e}tale}, \Lambda )$.
Proof. This follows from Lemmas 59.76.5 and 59.71.9. $\square$
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