Lemma 38.28.4. In Situation 38.28.1 let $K$ be as in Lemma 38.28.2. Then $K$ is pseudo-coherent relative to $A$.
Proof. Combinging Lemma 38.28.3 and Derived Categories of Schemes, Lemma 36.34.3 we see that $R\Gamma (X, K \otimes ^\mathbf {L} E)$ is pseudo-coherent in $D(A)$ for all pseudo-coherent $E$ in $D(\mathcal{O}_ X)$. Thus the lemma follows from More on Morphisms, Lemma 37.69.4. $\square$
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