Lemma 21.29.10. In Situation 21.29.1. Let $X$ be in $\mathcal{C}$.

1. for $\mathcal{F}'$ in $\mathcal{A}'_ X$ we have $H^ n_{\tau '}(X, \mathcal{F}') = H^ n_\tau (X, \epsilon _ X^{-1}\mathcal{F}')$,

2. for $K' \in D^+_{\mathcal{A}'_ X}(\mathcal{C}_{\tau '}/X)$ we have $H^ n_{\tau '}(X, K') = H^ n_\tau (X, \epsilon _ X^{-1}K')$.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).