Tame distillation and desingularization by p-alterations

Michael Temkin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We strengthen Gabber's l'-alteration theorem by avoiding all primes in- vertible on a scheme. In particular, we prove that any scheme X of finite type over a quasi-excellent threefold can be desingularized by a char(X)- alteration, i.e., an alteration whose order is only divisible by primes nonin- vertible on X. The main new ingredient in the proof is a tame distillation theorem asserting that, after enlarging, any alteration of X can be split into a composition of a tame Galois alteration and a char(X)-alteration. The proof of the distillation theorem is based on the following tameness theorem that we deduce from a theorem of M. Pank: if a valued field k of residue characteristic p has no nontrivial p-extensions, then any algebraic extension l/k is tame.

Original languageAmerican English
Pages (from-to)97-126
Number of pages30
JournalAnnals of Mathematics
Volume186
Issue number1
DOIs
StatePublished - 1 Jul 2017

Bibliographical note

Publisher Copyright:
© 2017 Department of Mathematics, Princeton University.

Keywords

  • Alterations
  • Resolution of singularities
  • Tame distillation
  • Valuations

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