Prismatic $F$-crystals and Wach modules
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917459572817920 |
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| author | Abhinandan |
| author_facet | Abhinandan |
| contents | We show that the category of analytic/completed prismatic $F$-crystals on the absolute prismatic site of a small (unramified at $p$) base ring is naturally equivalent to the category of relative Wach modules from the theory of $(φ, Γ)$-modules. The result is obtained by showing that the data of the Galois action on a Wach module is equivalent to the data of a prismatic stratification on the underlying $φ$-module. Along the way, we obtain new descent results for relative Wach modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18245 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prismatic $F$-crystals and Wach modules Abhinandan Number Theory Algebraic Geometry 14F20, 14F30, 14F40 We show that the category of analytic/completed prismatic $F$-crystals on the absolute prismatic site of a small (unramified at $p$) base ring is naturally equivalent to the category of relative Wach modules from the theory of $(φ, Γ)$-modules. The result is obtained by showing that the data of the Galois action on a Wach module is equivalent to the data of a prismatic stratification on the underlying $φ$-module. Along the way, we obtain new descent results for relative Wach modules. |
| title | Prismatic $F$-crystals and Wach modules |
| topic | Number Theory Algebraic Geometry 14F20, 14F30, 14F40 |
| url | https://arxiv.org/abs/2405.18245 |