The Stacks project

Definition 41.3.1. Let $A$, $B$ be Noetherian local rings. A local homomorphism $A \to B$ is said to be unramified homomorphism of local rings if

  1. $\mathfrak m_ AB = \mathfrak m_ B$,

  2. $\kappa (\mathfrak m_ B)$ is a finite separable extension of $\kappa (\mathfrak m_ A)$, and

  3. $B$ is essentially of finite type over $A$ (this means that $B$ is the localization of a finite type $A$-algebra at a prime).


Comments (2)

Comment #54 by Rankeya on

I think in (2) you want to be a finite separable extension of .


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Your email address will not be published.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 024M. Beware of the difference between the letter 'O' and the digit '0'.