Log prismatic $F$-crystals and purity
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912940562579456 |
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| author | Du, Heng Liu, Tong Moon, Yong Suk Shimizu, Koji |
| author_facet | Du, Heng Liu, Tong Moon, Yong Suk Shimizu, Koji |
| contents | Our goal is to study $p$-adic local systems on a rigid-analytic variety with semistable formal model. We prove that such a local system is semistable if and only if so are its restrictions to the points corresponding to the irreducible components of the special fiber. For this, the main body of the paper concerns analytic prismatic $F$-crystals on the absolute logarithmic prismatic site of a semistable $p$-adic log formal scheme. Analyzing Breuil-Kisin log prisms, we obtain a prismatic purity theorem and deduce the above purity theorem for semistable local systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Log prismatic $F$-crystals and purity Du, Heng Liu, Tong Moon, Yong Suk Shimizu, Koji Number Theory Algebraic Geometry Our goal is to study $p$-adic local systems on a rigid-analytic variety with semistable formal model. We prove that such a local system is semistable if and only if so are its restrictions to the points corresponding to the irreducible components of the special fiber. For this, the main body of the paper concerns analytic prismatic $F$-crystals on the absolute logarithmic prismatic site of a semistable $p$-adic log formal scheme. Analyzing Breuil-Kisin log prisms, we obtain a prismatic purity theorem and deduce the above purity theorem for semistable local systems. |
| title | Log prismatic $F$-crystals and purity |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2404.19603 |