The Jacobian ideal of a commutative ring and annihilators of cohomology

2016/10/09 by Iyengar, Srikanth B., Takahashi, Ryo
#13D03 #13D07 (Primary) 13D09 #16E30 #16E45 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.02599

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 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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