Vanishing of Ext and tor over fiber products

Saeed Nasseh, Sean Sather-Wagstaff

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

Consider a non-trivial fiber product R = S ×k T of local rings S, T with common residue field k. Given two finitely generated R-modules M and N, we show that if TorRi (M, N) = 0 = TorRi+1(M, N) for some i ≥ 5, then pdR (M) ≤ 1 or pdR (N) ≤ 1. From this, we deduce several consequences, for instance, that R satisfies the Auslander-Reiten Conjecture.

Original languageEnglish
Pages (from-to)4661-4674
Number of pages14
JournalProceedings of the American Mathematical Society
Volume145
Issue number11
DOIs
StatePublished - 2017

Scopus Subject Areas

  • General Mathematics
  • Applied Mathematics

Keywords

  • Auslander-Reiten
  • Ext-index
  • Ext-vanishing
  • Fiber product
  • Injective dimension
  • Projective dimension
  • Semidualizing complexes
  • Tor-vanishing

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