Desingularization of quasi-excellent schemes in characteristic zero

Michael Temkin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Scopus citations

Abstract

Grothendieck proved in EGA IV that if any integral scheme of finite type over a locally noetherian scheme X admits a desingularization, then X is quasi-excellent, and conjectured that the converse is probably true. We prove this conjecture for noetherian schemes of characteristic zero. Namely, starting with the resolution of singularities for algebraic varieties of characteristic zero, we prove the resolution of singularities for noetherian quasi-excellent Q-schemes.

Original languageAmerican English
Pages (from-to)488-522
Number of pages35
JournalAdvances in Mathematics
Volume219
Issue number2
DOIs
StatePublished - 1 Oct 2008
Externally publishedYes

Keywords

  • Desingularization
  • Quasi-excellent
  • Resolution
  • Singularities

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