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Nonvanishing cohomology and classes of Gorenstein rings

David A. Jorgensen·Liana M. Sega
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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 $n_M$ such that for all finitely generated $Λ$-modules $N$, if $\Ext_Λ^i(M,N)=0$ for all $i\gg 0$, then $\Ext_Λ^i(M,N)=0$ for all $i\geq n_M$. 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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David A. Jorgensen, Liana M. Sega. 2003-06-02. Nonvanishing cohomology and classes of Gorenstein rings. https://arxiv.org/abs/math/0306001

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