Lemma 114.4.16. In Algebraic and Formal Geometry, Situation 52.10.1 we have $H^ s_\mathfrak a(M) = \mathop{\mathrm{lim}}\nolimits H^ s_\mathfrak a(M/I^ nM)$.

Proof. This is immediate from Algebraic and Formal Geometry, Theorem 52.10.8. The original version of this lemma, which had additional assumptions, was superseded by the this theorem. $\square$

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