Lemma 58.19.2. In Situation 58.19.1. Assume one of the following holds

$\dim (A/\mathfrak p) \geq 2$ for every minimal prime $\mathfrak p \subset A$ with $f \not\in \mathfrak p$, or

every connected component of $U$ meets $U_0$.

Then

is a faithful functor.

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