Lemma 47.8.1 (0A6L)—The Stacks project

Loading [MathJax]/extensions/tex2jax.js

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

next lemma

numberstags

history
statistics
1 tag refers to this tag

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. $\square$

Comments (0)

There are also:

4 comment(s) on Section 47.8: Deriving torsion

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment