Definition 62.9.1. Let $f : X \to S$ be a morphism of schemes. Assume $S$ is locally Noetherian and $f$ is locally of finite type. Let $r \geq 0$ be an integer. We say a relative $r$-cycle $\alpha $ on $X/S$ is a *proper relative cycle* if the support of $\alpha $ (Remark 62.5.6) is contained in a closed subset $W \subset X$ proper over $S$ (Cohomology of Schemes, Definition 30.26.2). The group of all proper relative $r$-cycles on $X/S$ is denoted $c(X/S, r)$.

## Post a comment

Your email address will not be published. Required fields are marked.

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).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)