The Stacks project

Proposition 61.29.7. Let $X$ be a Noetherian scheme. Let $\Lambda $ be a Noetherian ring and let $I \subset \Lambda $ be an ideal. Let $K$ be an object of $D_{cons}(X, \Lambda )$. Then $K$ is adic constructible (Definition 61.29.4).

Proof. This is a consequence of Lemma 61.29.6 and the fact that a Noetherian scheme is locally connected (Topology, Lemma 5.9.6), and the definitions. $\square$

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