The Jacobian ideal of a commutative ring and annihilators of cohomology
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 Extd+1R(-,-), 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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