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arXiv · 1208.4458

Bass numbers over local rings via stable cohomology

Luchezar L. Avramov·Srikanth B. Iyengar
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Abstract

For any non-zero finite module M of finite projective dimension over a noetherian local ring R with maximal ideal m and residue field k, it is proved that the natural map Ext_R(k,M)-->Ext_R(k,M/mM) is non-zero when R is regular and is zero otherwise. A noteworthy aspect of the proof is the use of stable cohomology. Applications include computations of Bass series over certain local rings.

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Luchezar L. Avramov, Srikanth B. Iyengar. 2012-08-22. Bass numbers over local rings via stable cohomology. https://arxiv.org/abs/1208.4458

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