Lemma 58.24.1. In Situation 58.19.1 assume
A has a dualizing complex and is f-adically complete,
one of the following is true
A_ f is (S_2) and every irreducible component of X not contained in X_0 has dimension \geq 4, or
if \mathfrak p \not\in V(f) and V(\mathfrak p) \cap V(f) \not= \{ \mathfrak m\} , then \text{depth}(A_\mathfrak p) + \dim (A/\mathfrak p) > 3.
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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