Existence of slices in a tame context
  We study the ramification theory for actions involving group schemes, focusing on the tame ramification. We consider the notion of tame quotient stack introduced in [AOV] and the one of tame action introduced in [CEPT]. We establish a local Slice theorem for unramified actions and after proving some interesting lifting properties for linearly reductive group schemes, we establish a Slice theorem for actions by commutative group schemes inducing tame quotient stacks. Roughly speaking, we show that these actions are induced from an action of an extension of the inertia group on a finitely presented flat neighborhood. We finally consider the notion of tame action and determine how this notion is related to the one of tame quotient stack previously considered. 
Sophie Marques
math.AG math.AC math.CT math.GR math.NT