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

By M. Temkin. 2009

62 citations recorded by the source corpus.

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 desin- gularization. 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 and formal schemes, and complex or non-archimedean analytic spaces. Moreover, these functors easily generalize to non-compact setting by use of generalized convergent blow up sequences with regular centers.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ec25dbd4ac98395373ddb8f5235c2b246fa64de8

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In Algebra and Number Theory

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Citations in the corpus

Relative P-adic Hodge Theory: Foundations (2013, methodology): “In case X = Spa(A,A) for A a reduced normal affinoid algebra over K, one can prove that X is pro-sheafy by using Temkin’s resolution of singularities for affinoid algebras [123] to reduce to the case where A is smooth over K, then making a construction of imperfect period rings generalizing that of ”
Relative p-adic Hodge theory, II: Imperfect period rings (2016, methodology): “We may thus apply Temkin’s desingularization theorem for quasiexcellent Q-schemes [107] to produce a projective birational morphism f0 : Y0 → Spec(A) of schemes which analytifies to a morphism f : Y → X of rigid analytic spaces with Y smooth.”
Tropical and non-Archimedean limits of degenerating families of volume forms (2016, background): “y, and such that each E i is normal (which then implies that each non-empty E J is normal). Every model Xcontains a largest snc Zariski open subset X snc ˆX. By Temkin’s version of Hironaka’s theorem [Tem12], Xis dominated by an snc model X0such that the induced birational morphism : X0!Xis projecti”