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Let $f: Y\longrightarrow X$ be a smooth proper map of smooth proper schemes over $\mathbb{Q}$, and let $\mathcal{F} = R^1_\text{ét}\overline{f}_*\mathbb{Q}_p$ denote the derived pushforward of $\...

Suppose $A \rightarrow B$ is a faithfully flat map of rings. Then the Amitsur complex is exact: $0 \rightarrow A \rightarrow B \rightarrow B \otimes_A B \rightarrow \dots$ (the second map is $id \...