The monomial conjecture and order ideals II

Research output: Contribution to journalArticlepeer-review

Abstract

Let I be an ideal of height d in a regular local ring (R, m, k = R/m) of dimension n and let Ω denote the canonical module of R/. I. In this paper we first prove the equivalence of the following: the non-vanishing of the edge homomorhpism ηd:ExtRn-d(k,Ω)→ExtRn(k,R), the validity of the order ideal conjecture for regular local rings, and the validity of the monomial conjecture for all local rings. Next we prove several special cases of the order ideal conjecture/monomial conjecture.

Original languageEnglish (US)
Pages (from-to)123-138
Number of pages16
JournalJournal of Algebra
Volume454
DOIs
StatePublished - May 15 2016

Keywords

  • Commutative algebra
  • Edge homomorphism in a spectral sequence
  • Finite projective dimension
  • Monomial conjecture
  • Order ideal conjecture
  • Primary
  • Regular local ring
  • Secondary
  • Syzygies

ASJC Scopus subject areas

  • Algebra and Number Theory

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