Symmetry in the vanishing of Ext over Gorenstein rings

By Craig Huneke, David A. Jorgensen. 2003

100 citations recorded by the source corpus.

We investigate symmetry in the vanishing of Ext for finitely generated modules over local Gorenstein rings. In particular, we define a class of local Gorenstein rings, which we call AB rings, and show that for finitely generated modules $M$ and $N$ over an AB ring $R$, $\mathrm{Ext}^i_R(M,N)=0$ for all $i\gg 0$ if and only if $\mathrm{Ext}^i_R(N,M)=0$ for all $i\gg 0$.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d939d6efb89d8fab0d01cb7333857dc6dca3b259

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Algebras that satisfy Auslander’s condition on vanishing of cohomology (2008, background): “1 yields new proofs and modest generalizations of the main res ult in [23] on symmetric Ext-vanishing over commutative noetherian Gorenstein AC r ings; these are given in Appendix B.”
Nonvanishing cohomology and classes of Gorenstein rings (2003, background): “implies Exti R(M,N) = 0 for all i > dimR, for all ﬁnitely generated R-modules M and N. Let AB denote the class of all AB rings. It is shown in [3] (cf. also [14]) that CI ⊆ AB, and subsequently in [14] (cf. also [21]) it is shown that this inclusion is strict. Note that the condition deﬁning AB r”
Vanishing of Tate homology and depth formulas over local rings (2011, background): “Recall from Huneke and Jorgensen [18] that a local ring R is called AB if it is Gorenstein, and the following holds for all finitely generated R-modules M and N ,”