Functorial desingularization of quasi-excellent schemes in characteristic zero: the nonembedded case

Abstract

We prove that any reduced Noetherian quasi-excellent scheme of characteristic zero admits a strong desingularization which is functorial with respect to all regular morphisms. As a main application, we deduce that any reduced formal variety of characteristic zero admits a strong functorial desingularization. Also, we show that as an easy formal consequence of our main result one obtains strong functorial desingularization for many other spaces of characteristic zero including quasi-excellent stacks, formal schemes, and complex or nonarchimedean analytic spaces. Moreover, these functors easily generalize to noncompact settings by use of generalized convergent blow-up sequences with regular centers.