Trace ideals, conductors, and ideals of finite (phantom) projective dimension
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912206611808256 |
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| author | Kimura, Kaito |
| author_facet | Kimura, Kaito |
| contents | In this paper, we consider whether parameter test ideals, conductors, $F$-ideals, and trace ideals are contained in an ideal whose quotient ring has finite phantom projective dimension (for example, ideals generated by a system of parameters or ideals with finite projective dimension). One of the main results asserts that such inclusions do not exist in quasi-Gorenstein complete local domains. We also provide examples of Cohen-Macaulay local rings with good properties where such inclusions occur, thus answering negatively a question of Huneke-Swanson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trace ideals, conductors, and ideals of finite (phantom) projective dimension Kimura, Kaito Commutative Algebra 13A35, 13B22, 13D02, 13D05 In this paper, we consider whether parameter test ideals, conductors, $F$-ideals, and trace ideals are contained in an ideal whose quotient ring has finite phantom projective dimension (for example, ideals generated by a system of parameters or ideals with finite projective dimension). One of the main results asserts that such inclusions do not exist in quasi-Gorenstein complete local domains. We also provide examples of Cohen-Macaulay local rings with good properties where such inclusions occur, thus answering negatively a question of Huneke-Swanson. |
| title | Trace ideals, conductors, and ideals of finite (phantom) projective dimension |
| topic | Commutative Algebra 13A35, 13B22, 13D02, 13D05 |
| url | https://arxiv.org/abs/2501.03442 |