Lemma 48.28.3 (0E2V)—The Stacks project

Loading [MathJax]/extensions/tex2jax.js

Table of contents
Part 3: Topics in Scheme Theory
Chapter 48: Duality for Schemes
Section 48.28: Relative dualizing complexes
Lemma 48.28.3 (cite)

previous lemma
next lemma

numberstags

history
statistics
2 tags refer to this tag

Lemma 48.28.3. Let $X \to S$ be a morphism of schemes which is flat and locally of finite presentation. Let $(K, \xi )$ be a relative dualizing complex. Then $\mathcal{O}_ X \to R\mathop{\mathcal{H}\! \mathit{om}}\nolimits _{\mathcal{O}_ X}(K, K)$ is an isomorphism.

Proof. Looking affine locally this reduces using Lemma 48.28.2 to the algebraic case which is Dualizing Complexes, Lemma 47.27.5. $\square$

Comments (0)

There are also:

2 comment(s) on Section 48.28: Relative dualizing complexes

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