2
$\begingroup$

Let F be a finite type proper Deligne-Mumford Stack over a perfect field. Is it true that the coarse moduli space of F is proper?

$\endgroup$
  • 4
    $\begingroup$ The map from the stack to the space is a proper homeomorphism - so yes. Brian Conrad has a "modern" proof of Keel and Mori's theorem on the existence of coarse moduli spaces which you may find interesting (and can find on his webpage). $\endgroup$ – mdeland Apr 8 '11 at 12:31
  • 1
    $\begingroup$ mdeland: Your comment should be an answer. $\endgroup$ – S. Carnahan Apr 9 '11 at 15:48
  • $\begingroup$ @mdeland Doesn't this show only the other direction, namely that a DM-stack with proper coarse moduli is proper as well? $\endgroup$ – Lennart Meier May 25 '18 at 15:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.