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

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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.

Original languageAmerican English
Pages (from-to)2207-2254
Number of pages48
JournalDuke Mathematical Journal
Volume161
Issue number11
DOIs
StatePublished - Aug 2012

All Science Journal Classification (ASJC) codes

  • General Mathematics

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