Fontaine-Laffaille Theory over Power Series Rings
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910548327661568 |
|---|---|
| author | Hokaj, Christian |
| author_facet | Hokaj, Christian |
| contents | Let $k$ be a perfect field of characteristic $p > 2$. We extend the equivalence of categories between Fontaine-Laffaille modules and $\mathbb{Z}_p$ lattices inside crystalline representations with Hodge-Tate weights at most $p-2$ of Fontaine and Laffaille to the situation where the base ring is the power series ring over the Witt vectors $ W(k)[\![ t_1, \cdots , t_d]\!]$ and where the base ring is a $p$-adically complete ring that is étale over the Tate Algebra $W(k)\langle t_1^{\pm 1}, \cdots , t_d^{\pm 1}\rangle$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21327 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fontaine-Laffaille Theory over Power Series Rings Hokaj, Christian Number Theory 11F80 (Primary) 11F85 Let $k$ be a perfect field of characteristic $p > 2$. We extend the equivalence of categories between Fontaine-Laffaille modules and $\mathbb{Z}_p$ lattices inside crystalline representations with Hodge-Tate weights at most $p-2$ of Fontaine and Laffaille to the situation where the base ring is the power series ring over the Witt vectors $ W(k)[\![ t_1, \cdots , t_d]\!]$ and where the base ring is a $p$-adically complete ring that is étale over the Tate Algebra $W(k)\langle t_1^{\pm 1}, \cdots , t_d^{\pm 1}\rangle$. |
| title | Fontaine-Laffaille Theory over Power Series Rings |
| topic | Number Theory 11F80 (Primary) 11F85 |
| url | https://arxiv.org/abs/2407.21327 |