Moduli of semistable sheaves on projective Deligne-Mumford stacks -- Fabio Nironi, October 30, 2009

We introduce a notion of Gieseker stability for coherent sheaves on tame Deligne-Mumford stacks with projective moduli scheme and some chosen polarization. We prove that this stability condition is open, and pure dimensional semistable sheaves form a bounded family. We explicitly construct the moduli stack of semistable sheaves as a finite type global quotient, and study the moduli scheme of stable sheaves and its compactification. With this general machinery we are able to retrieve, as special cases, results of Lieblich and Yoshioka about moduli of twisted sheaves and results of Maruyama-Yokogawa about parabolic bundles.