Lemma 15.63.17. Let $R$ be a ring. Let $K, L$ be objects of $D(R)$.

If $K$ is $n$-pseudo-coherent and $H^ i(K) = 0$ for $i > a$ and $L$ is $m$-pseudo-coherent and $H^ j(L) = 0$ for $j > b$, then $K \otimes _ R^\mathbf {L} L$ is $t$-pseudo-coherent with $t = \max (m + a, n + b)$.

If $K$ and $L$ are pseudo-coherent, then $K \otimes _ R^\mathbf {L} L$ is pseudo-coherent.

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