Timeline for How do the invariants of a group scheme action compare to the invariants of the group action by global sections
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 15, 2021 at 8:11 | comment | added | Wilberd van der Kallen | If everything is affine and $G$ is smooth, then it suffices to take for $B=R$. | |
| Jan 14, 2021 at 17:52 | comment | added | LSpice | @RobPratt, I was just deliberating over whether "does" should be "do" in the title. I eventually decided that it's about the ring of invariants, not about the individual invariants, and so left it. But I think your edit does make the title read more smoothly. :-) | |
| Jan 14, 2021 at 17:49 | history | edited | RobPratt | CC BY-SA 4.0 |
added 35 characters in body; edited title
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| Jan 14, 2021 at 15:48 | comment | added | David E Speyer | While I'm here, I just wanted to say that this is not at all a stupid question, and neither are any of your others! | |
| Jan 14, 2021 at 15:48 | answer | added | David E Speyer | timeline score: 5 | |
| Oct 27, 2020 at 16:36 | comment | added | David E Speyer | Ah, found it. If (1) $k$ is infinite, (2) $G$ is connected and either (3a) $G$ is reductive or (3b) $k$ is perfect, then $G(k)$ is Zariski dense in $G$. mathoverflow.net/q/56192/297 | |
| Oct 27, 2020 at 15:52 | comment | added | LSpice | @DavidESpeyer is right; I definitely meant smooth connected, and there is a slight possibility I meant reductive. | |
| Oct 27, 2020 at 15:20 | comment | added | David E Speyer | I agree that the key thing to say is that, if $G(k)$ is Zariski dense in $G$, then $A^{G(k)} = A^G$. But I don't think your finite field criterion is the right one. For example, let $G = \mu_3$, the group of $3$-rd roots of unity, and let $k = \mathbb{R}$. @LSpice | |
| Oct 27, 2020 at 12:51 | comment | added | LSpice | A simple and unsatisfactory one: if $k$ is not an algebraic extension of a finite field, and $G$ is smooth, then $G(k)$ is Zariski dense, so $A^{G(k)} = A^G$. | |
| Oct 27, 2020 at 8:50 | history | edited | stupid_question_bot | CC BY-SA 4.0 |
added 5 characters in body
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| Oct 27, 2020 at 8:45 | history | asked | stupid_question_bot | CC BY-SA 4.0 |