Nonvanishing cohomology and classes of Gorenstein rings |
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| Authors: | David A Jorgensen Liana M ?ega |
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| Institution: | a Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
b Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA 94720-5070, USA |
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| 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 nM such that for all finitely generated Λ-modules N, if ExtΛi(M,N)=0 for all i?0, then ExtΛi(M,N)=0 for all i?nM. 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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| Keywords: | 13D07 |
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