Timeline for Is the GIT quotient of a finite map of varieties again a finite map?
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| Oct 15, 2023 at 16:26 | comment | added | Friedrich Knop | If $X$ and $Y$ are affine then this is certainly true. By assumption, every $f\in\mathcal{O}(X)^G$ satisfies an integrality equation over $\mathcal{O}(Y)$. Now apply the Reynolds operator to this equation and one gets an integrality equation over $\mathcal{O}(Y)^G$. So $\mathcal{O}(X)^G$ is integral hence finite over $\mathcal{O}(Y)^G$. The general case should follow with standard arguments. | |
| Oct 15, 2023 at 13:22 | history | asked | Joe Silverman | CC BY-SA 4.0 |