This is mostly a reference question. Suppose that I have an action of (say, finite) group $G$ on an algebraic stack $X$ (in my case it is a Deligne-Mumford stack, but this shouldn't matter). As far as I understand, in this case it makes sense to talk about the fixed points stack $X^G$ (which is not a closed substack of $X$). Does anybody know a good reference for this notion and various things related to it (tangent spaces etc.)?


A standard reference is

Romagny, Matthieu Group actions on stacks and applications. Michigan Math. J. 53 (2005), no. 1, 209–236.



  • $\begingroup$ Yes, great! I think in Graber-Pandharipande localisation on stack you define the fixed locus as the zeros of the vector field generated on the stack by the group action. But I still do not know a reference for these vector field generated by a group action on a stack. $\endgroup$
    – user100272
    Jan 29 '18 at 22:21

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