The Stacks project

Remark 101.51.3. We do not know whether Lemma 101.51.2 holds if we only assume $\mathcal{X}$ is locally Noetherian, i.e., we drop the assumption on the inertia being quasi-compact. In this case, if $x$ is a closed point, this is certainly true as follows from the following much simpler lemma.

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