The Stacks project

Situation 98.27.1. Let $S$ be a locally Noetherian scheme. Let $X'$ be an algebraic space locally of finite type over $S$. Let $T' \subset |X'|$ be a closed subset. Let $U' \subset X'$ be the open subspace with $|U'| = |X'| \setminus T'$. Let $W$ be a locally Noetherian formal algebraic space over $S$ with $W_{red}$ locally of finite type over $S$. Finally, we let

\[ g : X'_{/T'} \longrightarrow W \]

be a formal modification, see Algebraization of Formal Spaces, Definition 88.24.1. Recall that $X'_{/T'}$ denotes the formal completion of $X'$ along $T'$, see Formal Spaces, Section 87.14.


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Your email address will not be published.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 0GH8. Beware of the difference between the letter 'O' and the digit '0'.