MathOverflow is a question and answer site for professional mathematicians. 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

I'd be surprised if somebody proved the inverse Galois problem for $\mathbb{C}(x,y)$, but I wanted to make sure.

share|cite|improve this question
up vote 13 down vote accepted

Surely the inverse Galois problem is known over $\mathbf{C}(x)$: The Galois group of the maximal extension of $\mathbf{C}(x)$ unramified away from $n+1$ given primes of $\mathbf{C}[x]$ is the free profinite group on $n$ generators. Any finite group $G$ is a quotient of such a group, so there exists a finite Galois extension $L/\mathbf{C}(x)$ with Galois group $G$.

Then $L\otimes_{\mathbf{C}(x)}\mathbf{C}(x,y)$ is a finite Galois extension of $\mathbf{C}(x,y)$ with Galois group $G$.

share|cite|improve this answer
Whoops, silly me. – Makhalan Duff Jun 5 '10 at 2:36

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.