Lemma 23.8.9. Let $A \to B$ be a flat local homomorphism of Noetherian local rings. Then the following are equivalent

1. $B$ is a complete intersection,

2. $A$ and $B/\mathfrak m_ A B$ are complete intersections.

Proof. Now that the definition makes sense this is a trivial reformulation of the (nontrivial) Proposition 23.8.4. $\square$

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.

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 09Q7. Beware of the difference between the letter 'O' and the digit '0'.