Lemma 47.8.1 (0A6L)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 47: Dualizing Complexes
Section 47.8: Deriving torsion
Lemma 47.8.1 (cite)

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Lemma 47.8.1. Let $A$ be a ring and let $I \subset A$ be a finitely generated ideal. The functor $R\Gamma _ I$ is right adjoint to the functor $D(I^\infty \text{-torsion}) \to D(A)$ .

Proof. This follows from the fact that taking $I$ -power torsion submodules is the right adjoint to the inclusion functor $I^\infty \text{-torsion} \to \text{Mod}_ A$ . See Derived Categories, Lemma 13.30.3. $\square$

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