Lemma 58.24.2. Let $(A, \mathfrak m)$ be a Noetherian local ring. Let $f \in \mathfrak m$. Assume

$A$ is $f$-adically complete,

$f$ is a nonzerodivisor,

$H^1_\mathfrak m(A/fA)$ and $H^2_\mathfrak m(A/fA)$ are finite $A$-modules,

for every maximal ideal $\mathfrak p \subset A_ f$ purity holds for $(A_ f)_\mathfrak p$.

Then the restriction functor $\textit{FÉt}_ U \to \textit{FÉt}_{U_0}$ is essentially surjective.

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