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

Details Functorial desingularization of quasi-excellent schemes in characteristic zero: the non-embedded case Functorial desingularization of quasi-excellent schemes in characteristic zero: the non-embedded case

2009-04-09

arxiv.org/abs/0904.1592v2

Mathematics

Algebraic Geometry

35 pages, final version, section 3.2 in the first version was seriously modified

Scientific paper

We prove that any noetherian quasi-excellent scheme of characteristic zero admits a strong desingularization which is functorial with respect to all regular morphisms. We show that as an easy formal consequence of this result one obtains strong functorial desingularization for many other spaces of characteristic zero including quasi-excellent stacks and formal schemes, and complex and non-archimedean analytic spaces. Moreover, these functors easily generalize to non-compact setting by use of converging blow up hyper-sequences with regular centers.

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