---
date: 2022-02-09 12:00
modification date: Wednesday 9th February 2022 12:00:36
title: dualizing sheaf
aliases: [dualizing sheaf]

---

Tags: 
?
Refs:
[dualizable objects in a category](Unsorted/dualizable.md)


# dualizing sheaf

- Definition: a sheaf $\omega\in \Coh(X)$ is **dualizing** iff
$$
\mcf\in \Sh(X)^{\lf} \implies H^{n-i}\left(X; \mcf\dual \otimes \omega\right) \simeq H^{i}(X; \mcf)\dual
$$
	- If $X\in\smooth\Proj\Var$, then  $\omega$ is a representative of the [canonical sheaf](Unsorted/canonical%20bundle.md).