Nonvanishing cohomology and classes of Gorenstein rings

Details Nonvanishing cohomology and classes of Gorenstein rings Nonvanishing cohomology and classes of Gorenstein rings

2003-05-30

arxiv.org/abs/math/0306001v2

Mathematics

Commutative Algebra

16 pages

Scientific paper

We give counterexamples to the following conjecture of Auslander: given a finitely generated module $M$ over an Artin algebra $\Lambda$, there exists a positive integer $n_M$ such that for all finitely generated $\Lambda$-modules $N$, if $\Ext_{\Lambda}^i(M,N)=0$ for all $i\gg 0$, then $\Ext_{\Lambda}^i(M,N)=0$ 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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