Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.17852 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912888970543104 |
|---|---|
| author | Kim, Dongryul |
| author_facet | Kim, Dongryul |
| contents | We prove a descent result for finite projective modules, motivated by a question in perfectoid geometry. Given a commutative ring $A$, we formulate a descent problem for descending a finite projective module over the Novikov ring with coefficients in $A$ to a finite projective module over $A$. The main theorem of this paper is that all such descent data are effective. As an application, we prove for every perfect $\mathbb{F}_p$-algebra $A$, a vector bundle on $\operatorname{Spd} A$ always descends to a vector bundle on $\operatorname{Spec} A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17852 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Descending finite projective modules from a Novikov ring Kim, Dongryul Commutative Algebra Algebraic Geometry 13J05 (Primary) 13F25, 14G22 (Secondary) We prove a descent result for finite projective modules, motivated by a question in perfectoid geometry. Given a commutative ring $A$, we formulate a descent problem for descending a finite projective module over the Novikov ring with coefficients in $A$ to a finite projective module over $A$. The main theorem of this paper is that all such descent data are effective. As an application, we prove for every perfect $\mathbb{F}_p$-algebra $A$, a vector bundle on $\operatorname{Spd} A$ always descends to a vector bundle on $\operatorname{Spec} A$. |
| title | Descending finite projective modules from a Novikov ring |
| topic | Commutative Algebra Algebraic Geometry 13J05 (Primary) 13F25, 14G22 (Secondary) |
| url | https://arxiv.org/abs/2402.17852 |