Pseudo-quotients of algebraic actions and their application to character varieties

In this paper, we propose a weak version of quotient for the algebraic action group on variety, which shall call pseudo-quotient. They arise when focus purely topological properties good Geometric Invariant Theory (GIT) quotients regardless their properties. The flexibility granted by nature enables an easier identification in geometric constructions than classical GIT quotients. We obtain several results about interplay between pseudo-quotients and Additionally, show that characteristic zero are unique up to virtual class Grothendieck ring varieties. As application, compute [Formula: see text]-character varieties free groups surface as well parabolic counterparts with punctures Jordan type.