Lemma 85.6.2 (0D73)—The Stacks project

Processing math: 100%

Table of contents
Part 5: Topics in Geometry
Chapter 85: Simplicial Spaces
Section 85.6: Ringed simplicial sites
Lemma 85.6.2 (cite)

previous lemma
next lemma

numberstags

history
statistics
2 tags refer to this tag

Lemma 85.6.2. In Situation 85.3.3. Let $\mathcal{O}$ be a sheaf of rings on $\mathcal{C}_{total}$ . If $\mathcal{I}$ is injective in $\textit{Mod}(\mathcal{O})$ , then $\mathcal{I}_ n$ is a totally acyclic sheaf on $\mathcal{C}_ n$ .

Proof. This follows from Cohomology on Sites, Lemma 21.37.4 applied to the inclusion functor $\mathcal{C}_ n \to \mathcal{C}_{total}$ and its properties proven in Lemma 85.3.5. $\square$

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