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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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    $\begingroup$ Is this a duplicate of mathoverflow.net/questions/3190/… ? Note that BCnrd gave a great answer to that question: mathoverflow.net/a/14876 . $\endgroup$ – LSpice Jun 2 at 20:14
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    $\begingroup$ Does this answer your question? Is the fixed locus of a group action always a scheme? $\endgroup$ – Alex M. Jun 3 at 6:09
  • $\begingroup$ @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 ….) $\endgroup$ – LSpice Jun 3 at 16:20
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    $\begingroup$ @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. Jun 3 at 16:48
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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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    $\begingroup$ Specifically, see p. 37, just before Theorem 2.3. $\endgroup$ – LSpice Jun 2 at 20:12

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