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.
Comments (0)