Definition 15.101.3. Let $A$ be a discrete valuation ring. We say $A$ has *mixed characteristic* if the characteristic of the residue field of $A$ is $p > 0$ and the characteristic of the fraction field of $A$ is $0$. In this case we obtain an extension of discrete valuation rings $\mathbf{Z}_{(p)} \subset A$ and the *absolute ramification index* of $A$ is the ramification index of this extension.

## 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Your email address will not be published.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)