Nonvanishing cohomology and classes of Gorenstein rings

2003/05/30 by David A. Jorgensen, Jorgensen, David A., Liana M. Şega +2 · 1 citation
Mathematics · #13D03 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13D03

paper · pdf · doi:10.48550/arxiv.math/0306001

16 pages

openalex publication_date 2003/05/30 · arxiv created 2003/06/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer n_M such that for all finitely generated Λ-modules N, if \Ext_Λⁱ(M,N)=0 for all i≫ 0, then \Ext_Λⁱ(M,N)=0 for all i≥ n_M. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.

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