Lemma 21.30.10. In Situation 21.30.1. Let $X$ be in $\mathcal{C}$.
for $\mathcal{F}'$ in $\mathcal{A}'_ X$ we have $H^ n_{\tau '}(X, \mathcal{F}') = H^ n_\tau (X, \epsilon _ X^{-1}\mathcal{F}')$,
for $K' \in D^+_{\mathcal{A}'_ X}(\mathcal{C}_{\tau '}/X)$ we have $H^ n_{\tau '}(X, K') = H^ n_\tau (X, \epsilon _ X^{-1}K')$.
Proof. This follows from Lemma 21.30.8 by Remark 21.14.4. $\square$
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