On the injective dimension of unit Cartier and Frobenius modules
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929624984846336 |
|---|---|
| author | Blickle, Manuel Fink, Daniel Wheeler, Alexandria Zhang, Wenliang |
| author_facet | Blickle, Manuel Fink, Daniel Wheeler, Alexandria Zhang, Wenliang |
| contents | Let $R$ be a regular $F$-finite ring of prime characteristic $p$. We prove that the injective dimension of every unit Frobenius module $M$ in the category of unit Frobenius modules is at most $\operatorname{dim}(\operatorname{Supp}_R(M))+1$. We further show that for unit Cartier modules the same bound holds over any noetherian $F$-finite ring $A$ of prime characteristic $p$. This shows that $\dim A+1$ is a uniform upper bound for the injective dimension of any unit Cartier module over a noetherian $F$-finite ring $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08423 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the injective dimension of unit Cartier and Frobenius modules Blickle, Manuel Fink, Daniel Wheeler, Alexandria Zhang, Wenliang Commutative Algebra Algebraic Geometry 13D05, 13A35 Let $R$ be a regular $F$-finite ring of prime characteristic $p$. We prove that the injective dimension of every unit Frobenius module $M$ in the category of unit Frobenius modules is at most $\operatorname{dim}(\operatorname{Supp}_R(M))+1$. We further show that for unit Cartier modules the same bound holds over any noetherian $F$-finite ring $A$ of prime characteristic $p$. This shows that $\dim A+1$ is a uniform upper bound for the injective dimension of any unit Cartier module over a noetherian $F$-finite ring $A$. |
| title | On the injective dimension of unit Cartier and Frobenius modules |
| topic | Commutative Algebra Algebraic Geometry 13D05, 13A35 |
| url | https://arxiv.org/abs/2412.08423 |