Remark 82.7.3. In Situation 82.2.1 let $X/B$ be good. Assume $X$ is integral. In this case the function field $R(X)$ of $X$ is defined and is equal to the residue field of $X$ at its generic point. See Spaces over Fields, Definition 72.4.3. Combining this with Remark 82.2.3 we find that for any $x \in X$ the residue field $\kappa (x)$ is the function field of the unique integral closed subspace $Z \subset X$ whose generic point is $x$.
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Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)