Daniel Bergh: Functorial Destackification

By a destackification, we roughly mean a process which removes the stackiness from a smooth stack by repeatedly applying stacky blow-ups. We give an algorithm which produces such destackifications for smooth, tame stacks with abelian stabilisers in a functorial way. The techniques used are toric on a local scale and analogous to functorial resolution of singularities for varieties on a global scale. Possible applications are weak factorisation for Deligne--Mumford stacks in characteristic 0 and functorial resolution of tame, abelian quotient singularities for varities over fields of arbitrary characteristic.