Descent via Koszul extensions

Lars Winther Christensen, Sean Sather-Wagstaff

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Let R be a commutative noetherian local ring with completion over(R, ̂). We apply differential graded (DG) algebra techniques to study descent of modules and complexes from over(R, ̂) to R where R is either the henselization of R or a pointed étale neighborhood of R: We extend a given over(R, ̂)-complex to a DG module over a Koszul complex; we describe this DG module equationally and apply Artin approximation to descend it to R. This descent result for Koszul extensions has several applications. When R is excellent, we use it to descend the dualizing complex from over(R, ̂) to a pointed étale neighborhood of R; this yields a new version of P. Roberts' theorem on uniform annihilation of homology modules of perfect complexes. As another application we prove that the Auslander Condition on uniform vanishing of cohomology ascends to over(R, ̂) when R is excellent, henselian, and Cohen-Macaulay.

Original languageEnglish
Pages (from-to)3026-3046
Number of pages21
JournalJournal of Algebra
Volume322
Issue number9
DOIs
StatePublished - Nov 1 2009

Keywords

  • Artin approximation
  • Descent
  • Koszul extensions
  • Liftings
  • Semi-dualizing complexes
  • Semidualizing

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