Proposition 47.12.2 (0A6X)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 47: Dualizing Complexes
Section 47.12: Torsion versus complete modules
Proposition 47.12.2 (cite)

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

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

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

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

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