The Stacks project

Remark 15.93.7. With notation as in Lemma 15.93.6 we also see that the inverse system $H^ p(K_ n)$ has ML if and only if the inverse system $H^{p + 1}(K)[f^ n]$ has ML. This follows from the inverse system of short exact sequences $0 \to H^ p(K)/f^ nH^ p(K) \to H^ p(K_ n) \to H^{p + 1}(K)[f^ n] \to 0$ (see proof of the lemma) combined with Homology, Lemma 12.31.3 and Lemma 15.86.13.