Lemma 51.5.2 (0EF0)—The Stacks project

Processing math: 100%

Table of contents
Part 3: Topics in Scheme Theory
Chapter 51: Local Cohomology
Section 51.5: More general supports
Lemma 51.5.2 (cite)

previous lemma
next lemma

numberstags

history
statistics

Lemma 51.5.2. Let $A$ be a Noetherian ring. Let $T \subset \mathop{\mathrm{Spec}}(A)$ be a subset stable under specialization. The functor $RH^0_ T$ is the right adjoint to the functor $D(\text{Mod}_{A, T}) \to D(A)$ .

Proof. This follows from the fact that the functor $H^0_ T(-)$ is the right adjoint to the inclusion functor $\text{Mod}_{A, T} \to \text{Mod}_ A$ , see Derived Categories, Lemma 13.30.3. $\square$

Comments (0)

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