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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.04069 |
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| _version_ | 1866909894461882368 |
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| author | Pham, Dat |
| author_facet | Pham, Dat |
| contents | We give a new proof of a recent result of Tong Liu, which gives a general control on the torsion in the graded pieces of the so-called integral Hodge filtration associated to a crystalline Galois lattice. Our approach is stack-theoretic, and is inspired on the one hand by a result of Gee--Kisin on the shape of mod $p$ crystalline Breuil--Kisin modules, and on the other hand by the structures seen on the diffracted Hodge complex studied by Bhatt--Lurie. Along the way, we also obtain an explicit description of the Hodge--Tate locus in the Nygaard stack $\mathcal{O}_K^{\mathcal{N}}$ for a general extension $K/\mathbf{Q}_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prismatic $F$-gauges and a result of T. Liu Pham, Dat Number Theory Algebraic Geometry 11F80, 14D23 We give a new proof of a recent result of Tong Liu, which gives a general control on the torsion in the graded pieces of the so-called integral Hodge filtration associated to a crystalline Galois lattice. Our approach is stack-theoretic, and is inspired on the one hand by a result of Gee--Kisin on the shape of mod $p$ crystalline Breuil--Kisin modules, and on the other hand by the structures seen on the diffracted Hodge complex studied by Bhatt--Lurie. Along the way, we also obtain an explicit description of the Hodge--Tate locus in the Nygaard stack $\mathcal{O}_K^{\mathcal{N}}$ for a general extension $K/\mathbf{Q}_p$. |
| title | Prismatic $F$-gauges and a result of T. Liu |
| topic | Number Theory Algebraic Geometry 11F80, 14D23 |
| url | https://arxiv.org/abs/2411.04069 |