A Note on Symmetry in the Vanishing of Ext

Details A Note on Symmetry in the Vanishing of Ext A Note on Symmetry in the Vanishing of Ext

2009-04-30

arxiv.org/abs/0904.4858v1

Mathematics

Commutative Algebra

Scientific paper

Avramov and Buchweitz proved that for finitely generated modules $M$ and $N$ over a complete intersection local ring $R$, $\Ext^i_R(M,N)=0$ for all $i\gg 0$ implies $\Ext^i_R(N,M)=0$ for all $i\gg 0$. In this note we give some generalizations of this result. Indeed we prove the above mentioned result when (1) $M$ is finitely generated and $N$ is arbitrary, (2) $M$ is arbitrary and $N$ has finite length and (3) $M$ is complete and $N$ is finitely generated.

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