Does one need to work over an algebraic closed field in ordre to construct GIT quotients à la Mumford? If yes, why?
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10$\begingroup$ Have you looked in Mumford's book? $\endgroup$– AngeloCommented Nov 8, 2012 at 15:29
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2$\begingroup$ $X = {\rm Proj}\ R$, $X//G := {\rm Proj}\ R^G$ $\endgroup$– Allen KnutsonCommented Nov 8, 2012 at 20:16
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1 Answer
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Hey MBeasy,
you can construct the quotients over an arbitrary "not necessarily algebraically closed field", as Mumford states at the beginning of chapter 1.
Greetings
Daniel
