Remark 28.13.2. In [Hoobler-finite] a (locally Noetherian) scheme $X$ is called Japanese if for every $x \in X$ and every associated prime $\mathfrak p$ of $\mathcal{O}_{X, x}$ the ring $\mathcal{O}_{X, x}/\mathfrak p$ is Japanese. We do not use this definition since there exists a one dimensional Noetherian domain with excellent (in particular Japanese) local rings whose normalization is not finite. See [Example 1, Hochster-loci] or [Heinzer-Levy] or [ExposÃ© XIX, Traveaux]. On the other hand, we could circumvent this problem by calling a scheme $X$ Japanese if for every affine open $\mathop{\mathrm{Spec}}(A) \subset X$ the ring $A/\mathfrak p$ is Japanese for every associated prime $\mathfrak p$ of $A$.

## 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Your email address will not be published.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.

## Comments (0)