Lemma 52.5.4. Let (A, \mathfrak m) be a Noetherian local ring. Let I \subset A be an ideal. Let M be a finite A-module. Then
H^ i(R\Gamma _\mathfrak m(M)^\wedge ) = \mathop{\mathrm{lim}}\nolimits H^ i_\mathfrak m(M/I^ nM)
for all i where R\Gamma _\mathfrak m(M)^\wedge denotes the derived I-adic completion.
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