Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.13073 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909792540295168 |
|---|---|
| author | Mizuno, Yuki |
| author_facet | Mizuno, Yuki |
| contents | In this paper, we introduce the notions of dualizing complexes and balanced dualizing complexes over $\mathbb{Z}$-algebras. We prove that a noetherian connected $\mathbb{Z}$-algebra $A$ admits a balanced dualizing complex if and only if $A$ satisfies Artin-Zhang's $χ$-condition, has finite local cohomology dimension, and possesses symmetric derived torsion as a bigraded $A$-$A$-bimodule. As an application of our study of dualizing complexes, we show that any smooth noncommutative projective scheme associated to a $\mathbb{Z}$-algebra with a balanced dualizing complex admits a Serre functor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dualizing complexes over $\mathbb{Z}$-algebras Mizuno, Yuki Rings and Algebras Algebraic Geometry Category Theory 14A22, 16S38 In this paper, we introduce the notions of dualizing complexes and balanced dualizing complexes over $\mathbb{Z}$-algebras. We prove that a noetherian connected $\mathbb{Z}$-algebra $A$ admits a balanced dualizing complex if and only if $A$ satisfies Artin-Zhang's $χ$-condition, has finite local cohomology dimension, and possesses symmetric derived torsion as a bigraded $A$-$A$-bimodule. As an application of our study of dualizing complexes, we show that any smooth noncommutative projective scheme associated to a $\mathbb{Z}$-algebra with a balanced dualizing complex admits a Serre functor. |
| title | Dualizing complexes over $\mathbb{Z}$-algebras |
| topic | Rings and Algebras Algebraic Geometry Category Theory 14A22, 16S38 |
| url | https://arxiv.org/abs/2509.13073 |