Let $X$ be a smooth projective variety over $k$ and $G$ a finite group acting on $X$. Furthermore $\mathrm{char}(k)$ does not divide the order of $G$. Consider the quotient stack $[X/G]$. Is it right that this is a smooth, proper and connected DM stack with coarse moduli space. I mean this should be true since $X\rightarrow[X/G]$ is the cover and $X//G$ the moduli space right?
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$\begingroup$ Right! But this question doesn't belong on mathoverflow. $\endgroup$– guestFeb 5, 2014 at 15:37
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$\begingroup$ I think you mean "... DM stack with coarse moduli space $X//G$." Yes, this is correct. $\endgroup$– abxFeb 5, 2014 at 15:38
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$\begingroup$ With regard to guest's comment: I cannot think of a more appropriate place for the question than MathOverflow. $\endgroup$– Todd Trimble ♦Feb 5, 2014 at 17:24
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