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U_i -> U_i \times_X U_i
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aisejohan committed Jul 20, 2021
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Expand Up @@ -4046,7 +4046,7 @@ \section{Comparison with the \'etale site}
\epsilon^{-1}\mathcal{G}(U \times_X U \times_X U) =
\colim \mathcal{G}(U_i \times_X U_i \times_X U_i)
$$
hence we can find an $i$ and an element $g_i \in \mathcal{G}(U_i)$
hence we can find an $i$ and an element $g_i \in \mathcal{G}(U_i \times_X U_i)$
mapping to $g$ satisfying the cocycle condition.
The cocycle $g_i$ then defines a torsor for $\mathcal{G}$ on
$X_\etale$ whose pullback is isomorphic to $\mathcal{F}$
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