Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $f:X\longrightarrow S$ be a morphism of schemes. Assume $X$ and $S$ are integral.

Let $\eta$ be the generic point of $S$ and let $X_\eta\longrightarrow \textrm{Spec} \ K(S)$ be the induced morphism, where $K(S)$ denotes the function field of $S$.

Then, if $f$ is dominant, the function field $K(X_\eta)$ embeds canonically in $K(X)$. (Edit: Answered the question.)

share|cite|improve this question
If you answered your question then you can add your solution as an answer. – Adrián Barquero Jun 24 '11 at 18:20
Ok. I'll do that. – Narumi Jun 24 '11 at 22:48

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.