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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?

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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). – mdeland Apr 8 '11 at 12:31
mdeland: Your comment should be an answer. – S. Carnahan Apr 9 '11 at 15:48

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