Lemma 87.5.8 (0GX7)—The Stacks project

Processing math: 100%

Table of contents
Part 5: Topics in Geometry
Chapter 87: Formal Algebraic Spaces
Section 87.5: Taut ring maps
Lemma 87.5.8 (cite)

previous lemma
next lemma

numberstags

history
statistics

Lemma 87.5.8. Let $\varphi : A \to B$ be a continuous homomorphism of linearly topologized rings. If $\varphi$ is taut and $A$ is weakly pre-admissible, then $B$ is weakly pre-admissible.

Proof. Let $I \subset A$ be a weak ideal of definition. Then the closure $J$ of $IB$ is open and consists of topologically nilpotent elements by Lemma 87.4.10. Hence $J$ is a weak ideal of definition of $B$ . $\square$

Comments (0)

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