Compactification of Deligne-Mumford stacks                                                                                                                        
-- David Rydh, December 4, 2009

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I will show that every separated Deligne-Mumford
stack in characteristic zero can be embedded in a proper
Deligne-Mumford stack. The proof involves a          
certain class of "stacky blow-ups", Riemann-Zariski spaces and
"&eacute;talification" via stacky blow-ups. With appropriate tameness
assumptions, the result generalizes to     
arbitrary characteristic.