The Stacks project

Lemma 93.10.4. In Lemma 93.10.3 if $X$ and $Y$ are both proper over $k$, then $\text{Inf}(\mathcal{D}\! \mathit{ef}_{X \to Y})$ and $T\mathcal{D}\! \mathit{ef}_{X \to Y}$ are finite dimensional.

Proof. Omitted. Hint: argue as in Lemma 93.9.4 and use the exact sequence of the lemma. $\square$

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