Open loci results for commutative DG-rings

Liran Shaul

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Given a commutative noetherian non-positive DG-ring with bounded cohomology which has a dualizing DG-module, we study its regular, Gorenstein and Cohen-Macaulay loci. We give a sufficient condition for the regular locus to be open, and show that the Gorenstein locus is always open. However, both of these loci are often empty: we show that no matter how nice H0(A) is, there are examples where the Gorenstein locus of A is empty. We then show that the Cohen-Macaulay locus of a commutative noetherian DG-ring with bounded cohomology which has a dualizing DG-module always contains a dense open set. Our results imply that under mild hypothesis, eventually coconnective locally noetherian derived schemes are generically Cohen-Macaulay, but even in very nice cases, they need not be generically Gorenstein.

Original languageEnglish
Article number106922
JournalJournal of Pure and Applied Algebra
Volume226
Issue number5
DOIs
StatePublished - 1 May 2022
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory

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