Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $X$ and $Y$ be varieties over an algebraically closed field $K$, $\phi:Y \longrightarrow X$ be a finite etale cover , and let $K(X),K(Y)$ be the function fields of $X$ and $Y$ respectively. Then what is the relationship between $Gal(K(Y) / K(X))$ and $Aut(Y / X)$ where $Aut$ here means scheme automorphisms of $Y$ preserving $\phi$?

share|cite|improve this question
If $X$ and $Y$ are smooth, then the two groups are naturally isomorphic because of the correspondence betweeen dominant morphisms and field homomorphisms. – Zhen Lin Dec 30 '12 at 0:31

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.