Rigidity of Ext and Tor with Coefficients in Residue Fields of a Commutative Noetherian Ring

Lars Winther Christensen, Srikanth B. Iyengar, Thomas Marley

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let be a prime ideal in a commutative noetherian ring R. It is proved that if an R-module M satisfies (k (), M) = 0 for some n R, where k() is the residue field at , then (k (), M) = 0 holds for all i n. Similar rigidity results concerning (k (), M) are proved, and applications to the theory of homological dimensions are explored.

Original languageEnglish
Pages (from-to)305-321
Number of pages17
JournalProceedings of the Edinburgh Mathematical Society
Volume62
Issue number2
DOIs
StatePublished - May 1 2019

Keywords

  • Ext
  • Tor
  • flat dimension
  • injective dimension
  • rigidity

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