Functorial Desingularization of Quasi-excellent Schemes in Characteristic Zero: the Non-embedded Case
نویسنده
چکیده
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 hypersequences with regular centers.
منابع مشابه
Desingularization of Quasi-excellent Schemes in Characteristic Zero
For a Noetherian scheme X, let Xreg denote the regular locus of X. The scheme X is said to admit a resolution of singularities if there exists a blowup X ′ → X with center disjoint from Xreg and regular X ′. More generally, for a closed subscheme Z ⊂ X, let (X,Z)reg denote the set of points x ∈ Xreg such that, in an open neighborhood of x, Z is defined by an equation of the form t1 1 · · · · · ...
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