Reductive group-schemes, tame stacks, and stable maps -- Dan Abramovich

Joint work with M. Olsson and A. Vistoli. We describe finite linearly reductive group schemes in any characteristics, and use them to define tame Artin stacks, arguably an appropriate replacement in characteristic p for Deligne--Mumford stacks in characteristic 0. In particular there is a good and useful theory of stable maps into tame Artin stacks.