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Books on Inverse Galois problem usually deal directly with the number field case. I am looking for a good reference for a proof of the following fact:

Every finite group is realizable for any function field in one variable over a algebraically closed field of characteristic zero.

It is ok if the reference is a research paper, but I would prefer a survey/textbook if possible.

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This paper gives a proof of the Inverse Galois Problem over $\mathbb{C}(z)$ and mentions the classical proof which uses the Riemann Existence Theorem. Whether you can replace $\mathbb{C}$ with $\overline{\mathbb{Q}}$ though, I'm not sure.

http://www.math.uni-konstanz.de/~fehm/papers/Cz.pdf

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  • $\begingroup$ Thanks, I'll give it a look! $\endgroup$ Sep 17, 2015 at 11:18
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Groups as Galois groups by Helmut volklein is a nice reference for your question. Moreover, it is not too difficult to follow the proof.

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