# When a coherent sheaf on DM stack is locally free?

By | June 13, 2018

A coherent sheaf $\mathcal{F}$ on a variety $X$ is locally free if every fiber $\mathcal{F}|_x$ is of the same dimension. My question is if such theorem is also true on a Deligne-Mumford stack, or more generally an Artin Stack? If it is true, how to formulate it correctly?