Proposition 47.12.2. Let $A$ be a ring and let $I \subset A$ be a finitely generated ideal. The functors $R\Gamma _ Z$ and ${\ }^\wedge $ define quasi-inverse equivalences of categories

This is a special case of [Theorem 1.1, Porta-Liran-Yekutieli].

\[ D_{I^\infty \text{-torsion}}(A) \leftrightarrow D_{comp}(A, I) \]

**Proof.**
Follows immediately from Lemma 47.12.1.
$\square$

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