Stability of annihilators of cohomology and closed subsets defined by Jacobian ideals
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913520083271680 |
|---|---|
| author | Kimura, Kaito |
| author_facet | Kimura, Kaito |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17934 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of annihilators of cohomology and closed subsets defined by Jacobian ideals Kimura, Kaito Commutative Algebra 13D07, 13C15, 13N15 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. |
| title | Stability of annihilators of cohomology and closed subsets defined by Jacobian ideals |
| topic | Commutative Algebra 13D07, 13C15, 13N15 |
| url | https://arxiv.org/abs/2409.17934 |