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arXiv · 1610.02599

The Jacobian ideal of a commutative ring and annihilators of cohomology

Srikanth B. Iyengar·Ryo Takahashi
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Abstract

It is proved that for a ring $R$ that is either an affine algebra over a field, or an equicharacteristic complete local ring, some power of the Jacobian ideal of $R$ annihilates $\mathrm{Ext}^{d+1}_{R}(-,-)$, where $d$ is the Krull dimension of $R$. Sufficient conditions are identified under which the Jacobian ideal itself annihilates these Ext-modules, and examples are provided that show that this is not always the case. A crucial new idea is to consider a derived version of the Noether different of an algebra.

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Srikanth B. Iyengar, Ryo Takahashi. 2016-10-09. The Jacobian ideal of a commutative ring and annihilators of cohomology. https://arxiv.org/abs/1610.02599

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