Lemma 17.21.1 (01CG)—The Stacks project

Loading [MathJax]/extensions/tex2jax.js

Table of contents
Part 1: Preliminaries
Chapter 17: Sheaves of Modules
Section 17.21: Symmetric and exterior powers
Lemma 17.21.1 (cite)

next lemma

numberstags

Lemma 17.21.1. In the situation described above. The sheaf $\wedge ^ n\mathcal{F}$ is the sheafification of the presheaf

\[ U \longmapsto \wedge ^ n_{\mathcal{O}_ X(U)}(\mathcal{F}(U)). \]

See Algebra, Section 10.13. Similarly, the sheaf $\text{Sym}^ n\mathcal{F}$ is the sheafification of the presheaf

\[ U \longmapsto \text{Sym}^ n_{\mathcal{O}_ X(U)}(\mathcal{F}(U)). \]

Proof. Omitted. It may be more efficient to define $\text{Sym}(\mathcal{F})$ and $\wedge (\mathcal{F})$ in this way instead of the method given above. $\square$

Comments (0)

There are also:

3 comment(s) on Section 17.21: Symmetric and exterior powers

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