Lemma 24.29.3 (0FTQ)—The Stacks project

Processing math: 100%

Table of contents
Part 1: Preliminaries
Chapter 24: Differential Graded Sheaves
Section 24.29: Derived pushforward
Lemma 24.29.3 (cite)

previous definition
next lemma

numberstags

history
statistics
2 tags refer to this tag

Lemma 24.29.3. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\mathcal{A}$ , $\mathcal{B}$ be differential graded $\mathcal{O}$ -algebras. Let $\mathcal{N}$ be a differential graded $(\mathcal{A}, \mathcal{B})$ -bimodule. Then

$R\mathop{\mathcal{H}\! \mathit{om}}\nolimits _\mathcal {B}(\mathcal{N}, -) : D(\mathcal{B}, \text{d}) \longrightarrow D(\mathcal{A}, \text{d})$

is right adjoint to

$- \otimes _\mathcal {A}^\mathbf {L} \mathcal{N} : D(\mathcal{A}, \text{d}) \longrightarrow D(\mathcal{B}, \text{d})$

Proof. This follows from Derived Categories, Lemma 13.30.1 and Lemma 24.17.3. $\square$

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