I'm sorry if this is a trivial question, but it seems I can't find a clear answer. I have a finitely generated Poisson algebra $A$, the Poisson scheme $X=Spec(A)$ and an automorphism $g$.
What is the definition of the fixed point subscheme $X^g$?
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3$\begingroup$ Is this a duplicate of mathoverflow.net/questions/3190/… ? Note that BCnrd gave a great answer to that question: mathoverflow.net/a/14876 . $\endgroup$– LSpiceCommented Jun 2, 2020 at 20:14
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3$\begingroup$ Does this answer your question? Is the fixed locus of a group action always a scheme? $\endgroup$– Alex M.Commented Jun 3, 2020 at 6:09
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$\begingroup$ @AlexM., you and I are linking the same question. (I've never got the hang of when the post title expands in a Markdown link, so it's probably not clear what I'm linking ….) $\endgroup$– LSpiceCommented Jun 3, 2020 at 16:20
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2$\begingroup$ @LSpice: I didn't do it explicitly: I just voted to close this question as a duplicate (in the review queue), and the MO software automatically inserted that comment. Further close votes for the same reason would appear as upvotes of my comment. If the question got closed, my comment would be automatically deleted. $\endgroup$– Alex M.Commented Jun 3, 2020 at 16:48
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1 Answer
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This might be an unhelpful answer, but have you already considered the paper John Fogarty - Fixed points schemes?
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2$\begingroup$ Specifically, see p. 37, just before Theorem 2.3. $\endgroup$– LSpiceCommented Jun 2, 2020 at 20:12