Functorial factorization of birational maps for qe schemes in   characteristic 0
  We prove functorial weak factorization of projective birational morphisms of regular quasi-excellent schemes in characteristic 0 broadly based on the existing line of proof for varieties. From this general functorial statement we deduce factorization results for algebraic stacks, formal schemes, complex analytic germs, Berkovich analytic and rigid analytic spaces. 
Dan Abramovich and Michael Temkin
math.AG