Lemma 20.36.5. Let $A$ be a ring. Let $f \in A$. Let $X$ be a topological space. Let

be an inverse system of sheaves of $A$-modules. Let $p \geq 0$. Assume

either there is an $m \geq 1$ such that the image of $H^{p + 1}(X, \mathcal{F}_ m) \to H^{p + 1}(X, \mathcal{F}_1)$ is an $A$-module of finite length or $A$ is Noetherian and the intersection of the images of $H^{p + 1}(X, \mathcal{F}_ m) \to H^{p + 1}(X, \mathcal{F}_1)$ is a finite $A$-module,

$X$, $f$, $(\mathcal{F}_ n)$ satisfy condition (1) of Lemma 20.36.1.

Then the inverse system $M_ n = H^ p(X, \mathcal{F}_ n)$ satisfies the Mittag-Leffler condition.

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