Definition 31.13.1. Let $S$ be a scheme.

1. A locally principal closed subscheme of $S$ is a closed subscheme whose sheaf of ideals is locally generated by a single element.

2. An effective Cartier divisor on $S$ is a closed subscheme $D \subset S$ whose ideal sheaf $\mathcal{I}_ D \subset \mathcal{O}_ S$ is an invertible $\mathcal{O}_ S$-module.

There are also:

• 2 comment(s) on Section 31.13: Effective Cartier divisors

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).