Ogus-Vologodsky equivalence via stacks
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908939577196544 |
|---|---|
| author | Terentiuk, Gleb |
| author_facet | Terentiuk, Gleb |
| contents | Using the relative de Rham stack for a family $X \to S$ in characteristic $p,$ we reprove the (local and global) Ogus-Vologodsky equivalence. Moreover, we observe that a lift of $S$ is not necessary. Instead, we use a lift of $X$ to the second Witt vectors of $S.$ The main ingredient is that, for a quasi-syntomic family $X/S,$ the relative de Rham stack admits a structure of a torsor over $X'$ which is the analogue of the Azumaya property of the algebra of differential operators. This can be applied to families of (reasonable) algebraic stacks, which gives rise to a logarithmic version of the Cartier equivalence. Along the way, we also obtain a decompleted version of the global Cartier equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04317 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ogus-Vologodsky equivalence via stacks Terentiuk, Gleb Algebraic Geometry Using the relative de Rham stack for a family $X \to S$ in characteristic $p,$ we reprove the (local and global) Ogus-Vologodsky equivalence. Moreover, we observe that a lift of $S$ is not necessary. Instead, we use a lift of $X$ to the second Witt vectors of $S.$ The main ingredient is that, for a quasi-syntomic family $X/S,$ the relative de Rham stack admits a structure of a torsor over $X'$ which is the analogue of the Azumaya property of the algebra of differential operators. This can be applied to families of (reasonable) algebraic stacks, which gives rise to a logarithmic version of the Cartier equivalence. Along the way, we also obtain a decompleted version of the global Cartier equivalence. |
| title | Ogus-Vologodsky equivalence via stacks |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.04317 |