Functorial factorization of birational maps for qe schemes in characteristic 0

Abstract

We prove functorial weak factorization of projective birational morphisms of regular quasiexcellent 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, answering a present need in nonarchimedean geometry. Techniques developed for this purpose include a method for functorial factorization of toric maps, variation of GIT quotients relative to general noetherian qe schemes, and a GAGA theorem for Stein compacts.