Formal schemes and infinitesimal neighbourhoods
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916161990426624 |
|---|---|
| author | Bongiorno, Federico |
| author_facet | Bongiorno, Federico |
| contents | The aim of this article is to give a rigorous geometric interpretation of the completion of a ring with respect to an ideal. To this end, we define the infinitesimal neighbourhood of an immersion of formal schemes as the largest possible thickening. Further, we show that immersions of formal schemes locally of formal finite presentation admit the existence of infinitesimal neighbourhoods, which are locally given by completing with respect to an ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18813 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Formal schemes and infinitesimal neighbourhoods Bongiorno, Federico Algebraic Geometry The aim of this article is to give a rigorous geometric interpretation of the completion of a ring with respect to an ideal. To this end, we define the infinitesimal neighbourhood of an immersion of formal schemes as the largest possible thickening. Further, we show that immersions of formal schemes locally of formal finite presentation admit the existence of infinitesimal neighbourhoods, which are locally given by completing with respect to an ideal. |
| title | Formal schemes and infinitesimal neighbourhoods |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2305.18813 |