Growth in the minimal injective resolution of a local ring

Lars Winther Christensen, Janet Striuli, Oana Veliche

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

Let R be a commutative noetherian local ring with residue field k and assume that it is not Gorenstein. In the minimal injective resolution of R, the injective envelope E of the residue field appears as a summand in every degree starting from the depth of R. The number of copies of E in degree i equals the k-vector space dimension of the cohomology module ExtiR(k, R). These dimensions, known as Bass numbers, form an infinite sequence of invariants of R about which little is known. We prove that it is non-decreasing and grows exponentially if R is Golod, a non-trivial fiber product, or Teter, or if it has radical cube zero.

Original languageEnglish
Pages (from-to)24-44
Number of pages21
JournalJournal of the London Mathematical Society
Volume81
Issue number1
DOIs
StatePublished - Feb 2010

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