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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