3
$\begingroup$

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.)?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
4
$\begingroup$

A standard reference is

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

http://projecteuclid.org/euclid.mmj/1114021093

http://perso.univ-rennes1.fr/matthieu.romagny/articles/group_actions.pdf

Improve this answer
$\endgroup$
1
  • $\begingroup$ 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
    Commented Jan 29, 2018 at 22:21

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .