The Stacks project

Lemma 86.11.4. Consider the property $P$ on arrows of $\textit{WAdm}^{adic*}$ defined in Lemma 86.11.1. Then $P$ is stable under composition as defined in Formal Spaces, Remark 85.17.13.

Proof. The statement makes sense by Lemma 86.11.1. The easiest way to prove it is true is to show that (a) compositions of adic ring maps between adic topological rings are adic and (b) that compositions of continuous ring maps preserves the property of being topologically of finite type. We omit the details. $\square$


Comments (0)


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Your email address will not be published.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.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 0GBZ. Beware of the difference between the letter 'O' and the digit '0'.