Stability of annihilators of cohomology and closed subsets defined by Jacobian ideals
Abstract
Abstract Let R be a commutative Noetherian ring of dimension d. In this paper , we first show that some power of the cohomology annihilator annihilates the (d+1)-th Ext modules for all finitely generated modules when either R admits a dualizing complex or R is local. Next, we study the Jacobian ideal of affine algebras over a field and equicharacteristic complete local rings, and characterize the equidimensionality of the ring in terms of the singular locus and the closed subsets defined by the cohomology annihilator and the Jacobian ideal.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Publication details
- Journal / source
- The Quarterly Journal of Mathematics
- Volume
- 77
- Issue
- 3
- Pages
- 587–606
- Publication date
- 22 May 2026
- Language
- EN