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Timeline for Forms of algebraic varieties

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Mar 2, 2014 at 8:00 comment added ACL @JoeSilverman: You're right too! And since I heard you lecture about this GIT quotient, the fact that it is affine (hence quasiprojective) but that Weil's criterion did not apply still made me think how this could be so... (Remains to understand why!)
Mar 2, 2014 at 0:39 comment added Jérémy Blanc Yes, thanks to both of you for your examples. I was indeed mainly interested in schemes (and even in projective ones), but it is nice to see what happens in general.
Mar 2, 2014 at 0:31 comment added Joe Silverman You're right, it's not of the type Jeremy asked about. But after one's seen those types of examples, it's good to see other cases where it's not true. And even better is the example with an explanation, as you've given in terms of quotient stacks.
Mar 2, 2014 at 0:07 comment added ACL This is a nice example! But not really of the type Jérémy asked for, since the quotient stack $\mathop{\rm Rat}_d/\mathop{\rm PGL_2}$ is not a scheme. (The GIT quotient exists and is affine, but does not represent the quotient.)
Mar 1, 2014 at 23:22 history answered Joe Silverman CC BY-SA 3.0